summary numericals
DESCRIPTION
Numerical methods excel calculationsTRANSCRIPT
Name Yr/Crs Q1 Q2 Q3 Q4 SW FE Final Ave Final GradeLovren 3/ME 55.000000000000000 60.000000000000000 90.000000000000000 80.000000000000000 75.000000000000000 60.000000000000000 0.717500000000000 3.000000000000000
Lambert 3/CE 30.000000000000000 45.000000000000000 45.000000000000000 75.000000000000000 65.000000000000000 60.000000000000000 0.515000000000000 5.000000000000000Lallana 3/CE 50.000000000000000 35.000000000000000 45.000000000000000 50.000000000000000 65.000000000000000 70.000000000000000 0.497500000000000 5.000000000000000Rossiter 4/ME 55.000000000000000 60.000000000000000 80.000000000000000 90.000000000000000 95.000000000000000 95.000000000000000 0.762500000000000 2.500000000000000
Kelly 3/Me 60.000000000000000 60.000000000000000 85.000000000000000 60.000000000000000 95.000000000000000 95.000000000000000 0.737500000000000 2.750000000000000Sakho 3/EE 90.000000000000000 95.000000000000000 70.000000000000000 40.000000000000000 100.000000000000000 70.000000000000000 0.820000000000000 2.250000000000000
Sturridge 3/ECE 35.000000000000000 65.000000000000000 70.000000000000000 45.000000000000000 20.000000000000000 70.000000000000000 0.457500000000000 5.000000000000000Mignolet 3/ECE 55.000000000000000 60.000000000000000 90.000000000000000 80.000000000000000 75.000000000000000 60.000000000000000 0.717500000000000 3.000000000000000
Clyne 3/EE 50.000000000000000 50.000000000000000 50.000000000000000 20.000000000000000 40.000000000000000 60.000000000000000 0.430000000000000 5.000000000000000Henderson 3/EE 90.000000000000000 20.000000000000000 50.000000000000000 30.000000000000000 45.000000000000000 60.000000000000000 0.477500000000000 5.000000000000000
Quizzes Seat Work Finals60.00% 15.00% 25.00%
Low High Grade0.00% 69.99% 5.00
70.00% 73.00% 3.0073.01% 76.00% 2.7576.01% 80.00% 2.5080.01% 83.00% 2.2583.01% 86.00% 2.0086.01% 90.00% 1.7590.01% 93.00% 1.5093.01% 96.00% 1.2596.01% 100.00% 1.00
Final AverageMean Median Mode Variance Std. ev
0.613250000000000 0.616250000000000 0.717500000000000 0.020151312500000 0.141955318674574Skew Kurt Sum Min Max
0.058607461455378 2.107524441579260 6.132500000000000 0.430000000000000 0.820000000000000
Final GradeMean Median Mode Variance Std. ev
3.850000000000000 4.000000000000000 5.000000000000000 1.365000000000000 1.168332144554790Skew Kurt Sum Min Max
0.112374715317749 2.334604171338870 38.500000000000000 2.250000000000000 5.000000000000000
4.21x^3 − 3.18x^2 − 25.5x − 6X0 X2 X1 FX0 FX2 FX1 Remarks
2.000000000000000 1.750000000000000 1.500000000000000 1.400000000000000 6.323281250000000 10.886250000000000 Continue 2.000000000000000 1.875000000000000 1.750000000000000 1.400000000000000 2.881347656250000 6.323281250000000 Continue2.000000000000000 1.937500000000000 1.875000000000000 1.400000000000000 0.848684082031248 2.881347656250000 Continue2.000000000000000 1.968750000000000 1.937500000000000 1.400000000000000 0.248269958496088 0.848684082031248 Continue0.248269958496088 1.092884979248040 1.937500000000000 0.070450162539532 12.574904758670300 0.848684082031248 Continue0.248269958496088 0.670577468872066 1.092884979248040 0.070450162539532 8.400272611215420 12.574904758670300 Continue0.248269958496088 0.459423713684077 0.670577468872066 0.070450162539532 4.635855267219390 8.400272611215420 Continue0.248269958496088 0.353846836090083 0.459423713684077 0.070450162539532 2.438413071551100 4.635855267219390 Continue0.248269958496088 0.301058397293086 0.353846836090083 0.070450162539532 1.273888817036500 2.438413071551100 Continue0.248269958496088 0.274664177894587 0.301058397293086 0.070450162539532 0.676801553638718 1.273888817036500 Continue0.248269958496088 0.261467068195338 0.274664177894587 0.070450162539532 0.374754844533415 0.676801553638718 Continue0.248269958496088 0.254868513345713 0.261467068195338 0.070450162539532 0.222881121457748 0.374754844533415 Continue0.248269958496088 0.251569235920901 0.254868513345713 0.070450162539532 0.146734842892734 0.222881121457748 Continue0.248269958496088 0.249919597208495 0.251569235920901 0.070450162539532 0.108609746241378 0.146734842892734 Continue0.248269958496088 0.249094777852291 0.249919597208495 0.070450162539532 0.089534258184482 0.108609746241378 Continue0.248269958496088 0.248682368174190 0.249094777852291 0.070450162539532 0.079993285424603 0.089534258184482 Continue0.248269958496088 0.248476163335139 0.248682368174190 0.070450162539532 0.075221992636978 0.079993285424603 Continue0.248269958496088 0.248373060915614 0.248476163335139 0.070450162539532 0.072836144738139 0.075221992636978 Continue0.248269958496088 0.248321509705851 0.248373060915614 0.070450162539532 0.071643170424577 0.072836144738139 Continue0.248269958496088 0.248295734100970 0.248321509705851 0.070450162539532 0.071046670678273 0.071643170424577 Continue0.248269958496088 0.248282846298529 0.248295734100970 0.070450162539532 0.070748417657931 0.071046670678273 Continue0.248269958496088 0.248276402397309 0.248282846298529 0.070450162539532 0.070599290360985 0.070748417657931 Continue0.248269958496088 0.248273180446699 0.248276402397309 0.070450162539532 0.070524726515822 0.070599290360985 Continue0.248269958496088 0.248271569471393 0.248273180446699 0.070450162539532 0.070487444544067 0.070524726515822 Continue0.248269958496088 0.248270763983741 0.248271569471393 0.070450162539532 0.070468803545897 0.070487444544067 Continue0.248269958496088 0.248270361239915 0.248270763983741 0.070450162539532 0.070459483043740 0.070468803545897 Continue0.248269958496088 0.248270159868002 0.248270361239915 0.070450162539532 0.070454822791891 0.070459483043740 Continue0.248269958496088 0.248270059182045 0.248270159868002 0.070450162539532 0.070452492665776 0.070454822791891 Continue0.248269958496088 0.248270008839067 0.248270059182045 0.070450162539532 0.070451327602670 0.070452492665776 Continue0.248269958496088 0.248269983667578 0.248270008839067 0.070450162539532 0.070450745071105 0.070451327602670 Continue0.248269958496088 0.248269971081833 0.248269983667578 0.070450162539532 0.070450453805319 0.070450745071105 Continue0.248269958496088 0.248269964788961 0.248269971081833 0.070450162539532 0.070450308172425 0.070450453805319 Continue0.248269958496088 0.248269961642525 0.248269964788961 0.070450162539532 0.070450235355979 0.070450308172425 Continue
0.248269958496088 0.248269960069306 0.248269961642525 0.070450162539532 0.070450198947755 0.070450235355979 Continue0.248269958496088 0.248269959282697 0.248269960069306 0.070450162539532 0.070450180743643 0.070450198947755 Continue0.248269958496088 0.248269958889393 0.248269959282697 0.070450162539532 0.070450171641587 0.070450180743643 Continue0.248269958496088 0.248269958692741 0.248269958889393 0.070450162539532 0.070450167090559 0.070450171641587 Continue0.248269958496088 0.248269958594414 0.248269958692741 0.070450162539532 0.070450164815045 0.070450167090559 Continue0.248269958496088 0.248269958545251 0.248269958594414 0.070450162539532 0.070450163677290 0.070450164815045 Continue0.248269958496088 0.248269958520670 0.248269958545251 0.070450162539532 0.070450163108410 0.070450163677290 Continue0.248269958496088 0.248269958508379 0.248269958520670 0.070450162539532 0.070450162823971 0.070450163108410 Continue0.248269958496088 0.248269958502234 0.248269958508379 0.070450162539532 0.070450162681752 0.070450162823971 Continue0.248269958496088 0.248269958499161 0.248269958502234 0.070450162539532 0.070450162610642 0.070450162681752 Continue0.248269958496088 0.248269958497625 0.248269958499161 0.070450162539532 0.070450162575087 0.070450162610642 Continue0.248269958496088 0.248269958496857 0.248269958497625 0.070450162539532 0.070450162557309 0.070450162575087 Continue0.248269958496088 0.248269958496472 0.248269958496857 0.070450162539532 0.070450162548420 0.070450162557309 Continue0.248269958496088 0.248269958496280 0.248269958496472 0.070450162539532 0.070450162543977 0.070450162548420 Continue0.248269958496088 0.248269958496184 0.248269958496280 0.070450162539532 0.070450162541754 0.070450162543977 Continue0.248269958496088 0.248269958496136 0.248269958496184 0.070450162539532 0.070450162540643 0.070450162541754 Continue0.248269958496088 0.248269958496112 0.248269958496136 0.070450162539532 0.070450162540087 0.070450162540643 Continue0.248269958496088 0.248269958496100 0.248269958496112 0.070450162539532 0.070450162539809 0.070450162540087 Continue0.248269958496088 0.248269958496094 0.248269958496100 0.070450162539532 0.070450162539671 0.070450162539809 Continue0.248269958496088 0.248269958496091 0.248269958496094 0.070450162539532 0.070450162539601 0.070450162539671 Continue0.248269958496088 0.248269958496090 0.248269958496091 0.070450162539532 0.070450162539567 0.070450162539601 Continue0.248269958496088 0.248269958496089 0.248269958496090 0.070450162539532 0.070450162539550 0.070450162539567 Continue0.248269958496088 0.248269958496089 0.248269958496089 0.070450162539532 0.070450162539541 0.070450162539550 Continue0.248269958496088 0.248269958496089 0.248269958496089 0.070450162539532 0.070450162539537 0.070450162539541 Continue0.248269958496088 0.248269958496088 0.248269958496089 0.070450162539532 0.070450162539534 0.070450162539537 Continue0.248269958496088 0.248269958496088 0.248269958496088 0.070450162539532 0.070450162539533 0.070450162539534 Continue0.248269958496088 0.248269958496088 0.248269958496088 0.070450162539532 0.070450162539533 0.070450162539533 Terminate
12^x/(x-3)-sinx+15X0 X2 X1 FX0 FX2 FX1 Remarks
0.000000000000000 1.000000000000000 2.000000000000000 14.666666666666700 8.158529015192100 129.909297426826000 Continue 1 1.500000000000000 2 8.158529015192100 13.710307907706100 129.909297426826000 Continue1 1.250000000000000 1.5 8.158529015192100 1.288434455815620 13.710307907706100 Continue
1.25 1.375000000000000 1.5 1.288434455815620 4.731738237203490 13.710307907706100 Continue1.25 1.312500000000000 1.375 1.288434455815620 1.425833916233230 4.731738237203490 Continue1.25 1.281250000000000 1.3125 1.288434455815620 0.002290706818737 1.425833916233230 Continue1.25 1.265625000000000 1.28125 1.288434455815620 0.658819308204647 0.002290706818737 Continue
1.265625 1.273437500000000 1.28125 0.658819308204647 0.332304363637412 0.002290706818737 Continue1.2734375 1.277343750000000 1.28125 0.332304363637412 0.166030055540329 0.002290706818737 Continue
1.27734375 1.279296875000000 1.28125 0.166030055540329 0.082127152422073 0.002290706818737 Continue1.279296875 1.280273437500000 1.28125 0.082127152422073 0.039982802481314 0.002290706818737 Continue
1.2802734375 1.280761718750000 1.28125 0.039982802481314 0.018862219100578 0.002290706818737 Continue1.28076171875 1.281005859375000 1.28125 0.018862219100580 0.008289802256858 0.002290706818735 Continue
1.281005859375 1.281127929687500 1.28125 0.008289802256856 0.003000559660679 0.002290706818737 Continue1.2811279296875 1.281188964843750 1.28125 0.003000559660679 0.000355179457976 0.002290706818737 Continue
1.28118896484375 1.281219482421880 1.28125 0.000355179457976 0.000967700414678 0.002290706818737 Continue1.28118896484375 1.281204223632810 1.28121948242188 0.000355179457976 0.000306244662735 0.000967700414678 Continue1.28118896484375 1.281196594238280 1.28120422363281 0.000355179457973 0.000024471351427 0.000306244662735 Continue1.28119659423828 1.281200408935550 1.28120422363281 0.000024471351423 0.000140885667189 0.000306244662735 Continue1.28119659423828 1.281198501586910 1.28120040893555 0.000024471351423 0.000058206910770 0.000140885667189 Continue1.28119659423828 1.281197547912600 1.28119850158691 0.000024471351423 0.000016867717894 0.000058206910770 Continue1.28119659423828 1.281197071075440 1.2811975479126 0.000024471351423 0.000003801832209 0.000016867717894 Continue1.28119707107544 1.281197309494020 1.2811975479126 0.000003801832209 0.000006532938981 0.000016867717894 Continue1.28119707107544 1.281197190284730 1.28119730949402 0.000003801832209 0.000001365552421 0.000006532938981 Continue1.28119707107544 1.281197130680080 1.28119719028473 0.000003801832209 0.000001218140138 0.000001365552421 Continue1.28119713068008 1.281197160482410 1.28119719028473 0.000001218140136 0.000000073706079 0.000001365552423 Continue1.28119713068008 1.281197145581250 1.28119716048241 0.000001218140138 0.000000572217044 0.000000073706081 Continue1.28119714558125 1.281197153031830 1.28119716048241 0.000000572217044 0.000000249255484 0.000000073706081 Continue1.28119715303183 1.281197156757120 1.28119716048241 0.000000249255484 0.000000087774701 0.000000073706081 Continue1.28119715675712 1.281197158619760 1.28119716048241 0.000000087774701 0.000000007034313 0.000000073706081 Continue1.28119715861976 1.281197159551080 1.28119716048241 0.000000007034313 0.000000033335885 0.000000073706081 Continue1.28119715861976 1.281197159085420 1.28119715955108 0.000000007034313 0.000000013150787 0.000000033335885 Continue1.28119715861976 1.281197158852590 1.28119715908542 0.000000007034313 0.000000003058238 0.000000013150787 Continue1.28119715861976 1.281197158736180 1.28119715885259 0.000000007034313 0.000000001988036 0.000000003058238 Continue1.28119715873618 1.281197158794380 1.28119715885259 0.000000001988036 0.000000000535101 0.000000003058238 Continue1.28119715873618 1.281197158765280 1.28119715879438 0.000000001988035 0.000000000726464 0.000000000535099 Continue1.28119715876528 1.281197158779830 1.28119715879438 0.000000000726468 0.000000000095682 0.000000000535101 Continue1.28119715877983 1.281197158787110 1.28119715879438 0.000000000095682 0.000000000219709 0.000000000535101 Continue1.28119715877983 1.281197158783470 1.28119715878711 0.000000000095682 0.000000000062013 0.000000000219709 Continue1.28119715877983 1.281197158781650 1.28119715878347 0.000000000095682 0.000000000016835 0.000000000062013 Continue1.28119715878165 1.281197158782560 1.28119715878347 0.000000000016835 0.000000000022588 0.000000000062013 Continue
1.28119715878165 1.281197158782110 1.28119715878256 0.000000000016835 0.000000000002878 0.000000000022588 Continue1.28119715878165 1.281197158781880 1.28119715878211 0.000000000016835 0.000000000006981 0.000000000002878 Continue1.28119715878188 1.281197158781990 1.28119715878211 0.000000000006981 0.000000000002052 0.000000000002878 Continue1.28119715878199 1.281197158782050 1.28119715878211 0.000000000002052 0.000000000000414 0.000000000002878 Continue1.28119715878199 1.281197158782020 1.28119715878205 0.000000000002052 0.000000000000821 0.000000000000414 Continue1.28119715878202 1.281197158782040 1.28119715878205 0.000000000000815 0.000000000000203 0.000000000000416 Continue1.28119715878204 1.281197158782040 1.28119715878205 0.000000000000203 0.000000000000105 0.000000000000414 Continue1.28119715878204 1.281197158782040 1.28119715878204 0.000000000000203 0.000000000000000 0.000000000000105 Continue1.28119715878204 1.281197158782040 1.28119715878204 0.000000000000050 0.000000000000028 0.000000000000107 Continue1.28119715878204 1.281197158782040 1.28119715878204 0.000000000000000 0.000000000000000 0.000000000000000 Continue1.28119715878204 1.281197158782040 1.28119715878204 0.000000000000000 0.000000000000000 0.000000000000000 Terminate
4.21x^3 − 3.18x^2 − 25.5x − 6X0 X2 X1 FX0 FX2 FX1 Remarks
2.000000000000000 1.952681761184850 1.700000000000000 1.400000000000000 0.322558759519126 7.476070000000010 Continue1.700000000000000 1.964075426854890 1.952681761184850 7.476070000000010 0.080715371520334 0.322558759519126 Continue1.952681761184850 1.961794983139920 1.964075426854890 0.322558759519126 0.000580419638766 0.080715371520334 Continue1.964075426854890 1.961811264601710 1.961794983139920 0.080715371520334 0.000001030977039 0.000580419638766 Continue1.961794983139920 1.961811293573310 1.961811264601710 0.000580419638766 0.000000000013202 0.000001030977039 Continue1.961811264601710 1.961811293572940 1.961811293573310 0.000001030977039 0.000000000000000 0.000000000013202 Continue1.961811293573310 1.961811293572940 1.961811293572940 0.000000000013202 0.000000000000000 0.000000000000000 Continue1.961811293572940 #DIV/0! 1.961811293572940 0.000000000000000 #DIV/0! 0.000000000000000 Continue1.961811293572940 #DIV/0! #DIV/0! 0.000000000000000 #DIV/0! #DIV/0! Continue
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Continue#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Terminate
12^x/(x-3)-sinx+15X0 X2 X1 FX0 FX2 FX1 Remarks
0.000000000000000 2.253588883963390 1.000000000000000 14.666666666666700 348.062822787554000 8.158529015192100 Continue1.000000000000000 1.028710915926790 2.253588883963390 8.158529015192100 7.605812543471290 348.062822787554000 Continue2.253588883963390 1.054904376041270 1.028710915926790 348.062822787554000 7.058964178109750 7.605812543471290 Continue1.028710915926790 1.393021317337440 1.054904376041270 7.605812543471290 5.813767069841330 7.058964178109750 Continue1.054904376041270 1.240316106516230 1.393021317337440 7.058964178109750 1.663545179766250 5.813767069841330 Continue1.393021317337440 1.274289813766480 1.240316106516230 5.813767069841330 0.296197783827582 1.663545179766250 Continue1.240316106516230 1.281649272544700 1.274289813766480 1.663545179766250 0.019611742691334 0.296197783827582 Continue1.274289813766480 1.281192250828170 1.281649272544700 0.296197783827582 0.000212744263900 0.019611742691334 Continue1.281649272544700 1.281197155305600 1.281192250828170 0.019611742691337 0.000000150694003 0.000212744263910 Continue1.281192250828170 1.281197158782070 1.281197155305600 0.000212744263910 0.000000000001164 0.000000150694003 Continue1.281197155305600 1.281197158782040 1.281197158782070 0.000000150694003 0.000000000000000 0.000000000001164 Continue1.281197158782070 1.281197158782040 1.281197158782040 0.000000000001164 0.000000000000000 0.000000000000000 Continue1.281197158782040 #DIV/0! 1.281197158782040 0.000000000000000 #DIV/0! 0.000000000000000 Terminate
Equation 2x^3 - 11.7x^2 + 17.7x - 5 Terminate 0.0001
f(x):
Derived equation(s): Xo X1 f(Xo) f(x1) remarks Xo X1 f(Xo) f(x1) remarks[(11.7x^2 - 17.7x + 5)/2]^1/3 0 0.833333 0.833333 -0.270833 Continue 0 0.282486 0.282486 0.332687 Continue[(2x^3 + 17.7x - 5)/11.7]^1/2 0.833333 -0.270833 -0.270833 1.775326 Continue 0.282486 0.332687 0.332687 0.351487 Continue[(-2x^3 + 11.7x^2 + 5)/17.7] -0.270833 1.775326 1.775326 1.742095 Continue 0.332687 0.351487 0.351487 0.359243 Continue
1.775326 1.742095 1.742095 1.6122 Continue 0.351487 0.359243 0.359243 0.362555 Continue1.742095 1.6122 1.6122 1.145761 Continue 0.359243 0.362555 0.362555 0.363989 Continue
1.6122 1.145761 1.145761 0.013237 Continue 0.362555 0.363989 0.363989 0.364614 Continue1.145761 0.013237 0.013237 0.794626 Continue 0.363989 0.364614 0.364614 0.364886 Continue0.013237 0.794626 0.794626 -0.279524 Continue 0.364614 0.364886 0.364886 0.365006 Continue0.794626 -0.279524 -0.279524 1.81029 Continue 0.364886 0.365006 0.365006 0.365058 Terminate-0.279524 1.81029 1.81029 1.883419 Continue 0.365006 0.365058 0.365058 0.365081 Continue
2sin[sqrt(x)]-x Terminate 0.0001
Derived equation(s): Xo X1 f(Xo) f(x1) remarksf(x): 2sin[sqrt(x)] 1 1.682942 1.682942 1.925655 Continue
1.682942 1.925655 1.925655 1.966562 Continue1.925655 1.966562 1.966562 1.97169 Continue1.966562 1.97169 1.97169 1.972299 Continue1.97169 1.972299 1.972299 1.972371 Terminate
1.972299 1.972371 1.972371 1.97238 Terminate1.972371 1.97238 1.97238 1.972381 Terminate1.97238 1.972381 1.972381 1.972381 Terminate
1.972381 1.972381 1.972381 1.972381 Terminate1.972381 1.972381 1.972381 1.972381 Continue
Function 2x^3 - 11.7x^2 + 17.7x - 5 Terminate 0.0001
x0 x1 x2 f(x0) f(x1) f(x2) remarks1 2 1.882353 3 -0.4 0.200896 continue2 1.882353 1.921686 -0.4 0.200896 0.000283 continue
1.882353 1.921686 1.921741 0.200896 0.000283 -5.4E-07 terminate1.921686 1.921741 1.921741 0.000283 -5.4E-07 1E-12 terminate1.921741 1.921741 1.921741 -5.4E-07 1E-12 0 terminate1.921741 1.921741 1.921741 1E-12 0 0 terminate1.921741 1.921741 #DIV/0! 0 0 #DIV/0! #DIV/0!1.921741 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Transcedental Func.: 2sin[sqrt(x)]-x term. condition: 0.0001
x0 x1 x2 f(x0) f(x1) f(x2) remarks1 2 1.965412 0.682942 -0.02447 0.006141 continue2 1.965412 1.972351 -0.02447 0.006141 2.67E-05 terminate
1.965412 1.972351 1.972381 0.006141 2.67E-05 -3E-08 terminate1.972351 1.972381 1.972381 2.67E-05 -3E-08 1.42E-13 terminate1.972381 1.972381 1.972381 -3E-08 1.42E-13 0 terminate1.972381 1.972381 1.972381 1.42E-13 0 0 terminate1.972381 1.972381 #DIV/0! 0 0 #DIV/0! #DIV/0!1.972381 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
"-x^3 + 8x^2 - 4x - 5" Terminate 1.000000000000000r s b0 b1 c1 c2 c3
0.000000000000000 1.000000000000000 3.000000000000000 5.000000000000000 6.000000000000000 8.000000000000000 1.000000000000000det r det s delta r delta s r* s* er
37.000000000000000 19.000000000000000 0.637931034482759 0.327586206896552 0.637931034482759 0.672413793103448 100.000000000000000r s b0 b1 c1 c2 c3
0.637931034482759 0.672413793103448 0.034282873426545 0.024078478002379 3.641200951248510 6.724137931034480 1.000000000000000det r det s delta r delta s r* s* er
0.127624133830828 0.206444291589904 0.002612292050496 0.004225633237248 0.635318742432263 0.676639426340696 0.411178181284987r s b0 b1 c1 c2 c3
0.635318742432263 0.676639426340696 0.034282873426545 0.024078478002379 3.641200951248510 6.724137931034480 1.000000000000000det r det s delta r delta s r* s* er
0.127624133830828 0.206444291589904 0.002612292050496 0.004225633237248 0.632706450381767 0.680865059577944 0.412875836641052r s b0 b1 c1 c2 c3
0.632706450381767 0.680865059577944 0.015317385289421 0.002280608631696 0.674358817709000 6.729362515135470 1.000000000000000det r det s delta r delta s r* s* er
0.000029656948407 0.100795629764823 0.000000664805521 0.002259487060951 0.632705785576246 0.683124546638895 0.000105073406387r s b0 b1 c1 c2 c3
0.632705785576246 0.683124546638895 0.003775429559774 0.019530908878501 3.560620729888300 6.734587099236470 1.000000000000000det r det s delta r delta s r* s* er
0.127757177409740 0.005895050328827 0.002611804872232 0.000120515508272 0.635317590448478 0.683004031130623 0.411102244215863
Roots1.200063824123940
1.000000000000000 8.000000000000000 4.000000000000000 5.0000000000000000.000000000000000 1.200063824123940 8.160357411020530 4.992694424391670
1.000000000000000 6.799936175876060 4.160357411020530 0.007305575608331
1.000000000000000 6.798659141522900 4.167507009570290
Roots
0.565887767572416 7.364546909095320
%det D
2.000000000000000
continue
1.000000000000000 8.000000000000000 4.000000000000000es r = 0.000000000000000 0.000000000000000 0.000000000000000
48.717948717948700 s = 1.000000000000000 0.000000000000000 1.000000000000000det D 1.000000000000000 8.000000000000000 5.000000000000000
1.759719062001100
terminate
r = 0.000000000000000 0.000000000000000 0.000000000000000es s = 1.000000000000000 0.000000000000000 1.000000000000000
0.624502958702872 1.000000000000000 8.000000000000000 6.000000000000000det D
1.763572399945210
terminate
1.000000000000000 8.000000000000000 4.000000000000000es 0.637931034482759 0.637931034482759 4.696492271105830
0.620627123951284 0.672413793103448 0.000000000000000 0.672413793103448det D 1.000000000000000 7.362068965517240 0.024078478002379
1.767421197866110
terminate
0.637931034482759 0.637931034482759 4.289536266349580es 0.672413793103448 0.000000000000000 0.672413793103448
0.330757703272100 1.000000000000000 6.724137931034480 3.641200951248510det D
1.769975931377950
terminatees 1.000000000000000 8.000000000000000 4.000000000000000
0.017644919031022 0.635318742432263 0.635318742432263 4.6789200349723900.676639426340696 0.000000000000000 0.676639426340696
1.000000000000000 7.364681257567740 0.0022806086316960.635318742432263 0.635318742432263 0.0000000000000000.676639426340696 0.000000000000000 0.676639426340696
1.000000000000000 6.729362515135470 0.674358817709000
5.000000000000000 1.000000000000000 8.000000000000000 4.000000000000000 5.0000000000000000.000000000000000 0.632706450381767 0.632706450381767 4.661334150699440 0.0123573320292468.000000000000000 0.680865059577944 0.000000000000000 0.680865059577944 5.0161327615890203.000000000000000 1.000000000000000 7.367293549618230 0.019530908878501 0.003775429559774
0.632706450381767 0.632706450381767 4.2610166983447500.680865059577944 0.000000000000000 0.680865059577944
1.000000000000000 6.734587099236470 3.560620729888300
5.000000000000000 1.000000000000000 8.000000000000000 4.000000000000000 5.0000000000000000.015360408380828 0.632705785576246 0.632705785576246 4.661329673508310 0.0137897423256184.950356718192630 0.683124546638895 0.000000000000000 0.683124546638895 5.0327795201835800.034282873426545 1.000000000000000 7.367294214423750 0.021794873130580 0.0189897778579602.322835089589570 0.632705785576246 0.632705785576246 4.2610130624066604.521403091557670 0.683124546638895 0.000000000000000 0.683124546638895
1.000000000000000 6.734588428847510 3.556093642637180
5.0000000000000000.0014489134078694.9832337013027100.015317385289421
x^3-4x^2-x+3 f(x0) f(x1) f(x2)Terminate |(x3-x2)/x2|*100% < 0.0001 7.000000000000000 9.000000000000000 1.000000000000000
9.000000000000000 1.000000000000000 0.166736341844635x0 x1 x2 h0 h1 δ0 remarks 1.000000000000000 0.166736341844635 0.034121740301156
2.000000000000000 3.000000000000000 4.000000000000000 1.000000000000000 1.000000000000000 2.000000000000000continue
0.166736341844635 0.034121740301156 0.000001418255748δ1 a b c D x3 0.034121740301156 0.000001418255748 0.000000000001943
8.000000000000000 5.000000000000000 13.000000000000000 1.000000000000000 13.747727084867500 4.074772708486750 0.000001418255748 0.000000000001943 0.000000000000004x0 x1 x2 h0 h1 δ0 remarks
3.000000000000000 4.000000000000000 4.074772708486750 1.000000000000000 0.074772708486752 8.000000000000000continueδ1 a b c D x3
15.603772625828500 7.074772708486750 16.132772543170200 0.166736341844635 15.985864476045200 4.062305380603860x0 x1 x2 h0 h1 δ0 remarks
4.000000000000000 4.074772708486750 4.062305380603860 0.074772708486752 0.012467327882896 15.603772625828500continueδ1 a b c D x3
16.110756373172100 8.137078089082810 16.009308752626700 0.034121740301156 16.043957485558100 4.064434445395420x0 x1 x2 h0 h1 δ0 remarks
4.074772708486750 4.062305380603860 4.064434445395420 0.012467327882896 0.002129064791563 16.110756373172100terminateδ1 a b c D x3
16.025966978841900 8.201512534663290 16.043428530417000 0.000001418255748 16.043429980461400 4.064434533796450x0 x1 x2 h0 h1 δ0 remarks
4.062305380603860 4.064434445395420 4.064434533796450 0.002129064791563 0.000000088401035 16.025966978841900terminateδ1 a b c D x3
16.043407252858400 8.191178576164370 16.043407976967100 0.000000000001943 16.043407976969100 4.064434533796580x0 x1 x2 h0 h1 δ1 remarks
4.064434445395420 4.064434533796450 4.064434533796580 0.000000088401035 0.000000000000121 0.000000000000000#DIV/0!δ2 a b c D x4
0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 #DIV/0!
x^3-4x^2-x+3Terminate |(x3-x2)/x2|*100% < 0.0001
x0 x1 x2 h02.000000000000000 1.000000000000000 0.000000000000000 1.000000000000000
δ1 a b c4.000000000000000 7.000000000000000 3.000000000000000 3.000000000000000
x0 x1 x2 h01.000000000000000 0.000000000000000 0.903117911499497 1.000000000000000
δ1 a b c3.428093608069200 5.903117911499500 8.759305127637900 0.095972739744231
x0 x1 x2 h00.000000000000000 0.903117911499497 0.874226344739932 0.903117911499497
δ1 a b c8.478800159505650 5.777344256239440 8.311883632233520 0.148993081105135
x0 x1 x2 h00.903117911499497 0.874226344739932 0.891933713617266 0.028891566759565
δ1 a b c8.404209634959160 6.669277969857220 8.522305000116890 0.000176640976473
x0 x1 x2 h00.874226344739932 0.891933713617266 0.891954440182603 0.017707368877334
δ1 a b c8.522245324265330 6.658114498981450 8.522383324110530 0.000000004101934
x0 x1 x2 h00.891933713617266 0.891954440182603 0.891954440663917 0.000020726565338
δ2 a b c6232948982.620740000000000 300715730880513.000000000000000 6233093721.041530000000000 3.000000000000000
x^3-4x^2-x+3 f(x0) f(x1) f(x2)|(x3-x2)/x2|*100% < 0.0001 19.000000000000000 1.000000000000000 3.000000000000000
1.000000000000000 3.000000000000000 0.095972739744231h1 δ0 remarks 3.000000000000000 0.095972739744231 0.148993081105135
1.000000000000000 18.000000000000000#DIV/0!
0.095972739744231 0.148993081105135 0.000176640976473D x3 0.148993081105135 0.000176640976473 0.000000004101934
9.643650760992960 0.903117911499497 0.000176640976473 0.000000004101934 0.000000000000000h1 δ0 remarks 0.000000004101934 0.000000000000000 3.000000000000000
0.903117911499497 4.000000000000000continueD x3
8.628978660482600 0.874226344739932h1 δ0 remarks
0.028891566759565 3.428093608069200continueD x3
8.516486763986670 0.891933713617266h1 δ0 remarks
0.017707368877334 8.478800159505650continueD x3
8.522581462568090 0.891954440182603h1 δ0 remarks
0.000020726565338 8.404209634959160terminateD x3
8.522383330519800 0.891954440663917h1 δ1 remarks
0.000000000481313 0.000197907095599continueD x4
6232804244.199940000000000 0.891933713617266
x^3-4x^2-x+3Terminate |(x3-x2)/x2|*100% < 0.0001
x0 x1 x2 h01.000000000000000 3.000000000000000 5.000000000000000 2.000000000000000
δ1 a b c16.000000000000000 5.000000000000000 26.000000000000000 23.000000000000000
x0 x1 x2 h03.000000000000000 5.000000000000000 3.869693845669910 2.000000000000000
δ1 a b c22.844224304885500 7.869693845669910 13.949060918431100 2.820967322709120
x0 x1 x2 h05.000000000000000 3.869693845669910 4.008326746801310 1.130306154330090
δ1 a b c14.040128741984500 8.878020592471270 15.270914493023100 0.874543542949459
x0 x1 x2 h03.869693845669910 4.008326746801310 4.063805909548070 0.138632901131400
δ1 a b c15.581733075254000 7.941826502020700 16.022338960266100 0.010082037790881
x0 x1 x2 h04.008326746801310 4.063805909548070 4.064434962221180 0.055479162746759
δ1 a b c16.038261363961200 8.136567618322670 16.043379693571400 0.000006873392160
x0 x1 x2 h04.063805909548070 4.064434962221180 4.064434533795630 0.000629052673110
δ2 a b c7002383.608395020000000 11139219692.156600000000000 6997611.282149340000000 3.000000000000000
x^3-4x^2-x+3 f(x0) f(x1)|(x3-x2)/x2|*100% < 0.0001 1.000000000000000 9.000000000000000
9.000000000000000 23.000000000000000h1 δ0 remarks 23.000000000000000 2.820967322709120
2.000000000000000 4.000000000000000continue
2.820967322709120 0.874543542949459D x3 0.874543542949459 0.010082037790881
14.696938456699100 3.869693845669910 0.010082037790881 0.000006873392160h1 δ0 remarks 0.000006873392160 0.000000000015106
1.130306154330090 16.000000000000000continueD x3
16.833802221112800 4.008326746801310h1 δ0 remarks
0.138632901131400 22.844224304885500continueD x3
16.256004791660700 4.063805909548070h1 δ0 remarks
0.055479162746759 14.040128741984500continueD x3
16.032330614647100 4.064434962221180h1 δ0 remarks
0.000629052673110 15.581733075254000terminateD x3
16.043372721744600 4.064434533795630h1 δ1 remarks
0.000000428425543 0.010926600522141continueD x4
7007155.934640640000000 4.063805909547090
f(x2)23.0000000000000002.8209673227091200.8745435429494590.0100820377908810.0000068733921600.0000000000151063.000000000000000
Lower ArrayMatrix 3.000000000000000 2.000000000000000 1.000000000000000 10.000000000000000 L11
2.000000000000000 6.000000000000000 4.000000000000000 44.000000000000000 3.0000000000000001.000000000000000 2.000000000000000 5.000000000000000 26.000000000000000 L21
2.000000000000000Crout's L31
1.000000000000000
Lower ArrayMatrix 7.000000000000000 2.000000000000000 3.000000000000000 12.000000000000000 L11
2.000000000000000 5.000000000000000 3.000000000000000 20.000000000000000 1.0000000000000001.000000000000000 1.000000000000000 6.000000000000000 26.000000000000000 L21
2.000000000000000Doolittle L31
1.000000000000000
Lower Array Upper ArrayL12 L13 U11 U12 U13
0.000000000000000 0.000000000000000 1.000000000000000 0.666666666666667 0.333333333333333L22 L23 U21 U22 U23
7.333333333333330 0.000000000000000 0.000000000000000 1.000000000000000 0.636363636363637L32 L33 U31 U32 U33
2.666666666666670 3.636363636363640 0.000000000000000 0.000000000000000 1.000000000000000
Lower Array Upper ArrayL12 L13 U11 U12 U13
0.000000000000000 0.000000000000000 1.000000000000000 2.000000000000000 3.000000000000000L22 L23 U21 U22 U23
1.000000000000000 0.000000000000000 0.000000000000000 1.000000000000000 3.000000000000000L32 L33 U31 U32 U33
3.000000000000000 1.000000000000000 0.000000000000000 0.000000000000000 1.000000000000000
Terminate 0.100000000000000Given: x1 x2 x3 x4 xn
2.000000000000000 4.000000000000000 9.000000000000000 16.000000000000000 30.0000000000000004.000000000000000 9.000000000000000 16.000000000000000 25.000000000000000 54.0000000000000009.000000000000000 6.000000000000000 25.000000000000000 36.000000000000000 86.000000000000000
16.000000000000000 25.000000000000000 36.000000000000000 49.000000000000000 126.000000000000000
K X1 X2 X30.000000000000000 0.000000000000000 0.000000000000000 0.0000000000000001.000000000000000 15.000000000000000 6.000000000000000 3.4400000000000002.000000000000000 33.051428571428600 13.925079365079400 7.1028571428571403.000000000000000 138.133832199546000 55.303219954648500 30.0782802721088004.000000000000000 436.453019241983000 180.217506360004000 96.5499296404276005.000000000000000 1552.691721221100000 629.533864412462000 337.5160529749640006.000000000000000 5226.642364588140000 2139.583330475930000 1150.0925786262400007.000000000000000 18058.316661822700000 7355.760286906900000 3944.5032620354400008.000000000000000 61613.347526582000000 25159.647327209400000 13512.9176763634000009.000000000000000 211502.128882970000000 86259.794452056100000 46287.307311384700000
10.000000000000000 723882.497104058000000 295410.237396947000000 158594.98162013100000011.000000000000000 2481124.481739790000000 1012223.879112350000000 543289.68207068400000012.000000000000000 8498121.425814350000000 3467482.752465420000000 1861334.42210217000000013.000000000000000 29117008.464013500000000 11879745.835357100000000 6376607.16461698000000014.000000000000000 99746482.678077200000000 40698005.556723200000000 21845867.88551610000000015.000000000000000 341730760.289592000000000 139428710.893439000000000 74841357.70215950000000016.000000000000000 1170720288.960210000000000 477666624.944219000000000 256399779.93112900000000017.000000000000000 4010797366.537250000000000 1636442344.567770000000000 878399014.00485900000000018.000000000000000 13740550841.319000000000000 5606282697.136840000000000 3009309919.95875000000000019.000000000000000 47073836515.531400000000000 19206579288.472400000000000 10309593917.58750000000000020.000000000000000 161270174151.748000000000000 65799817549.065100000000000 35319651904.30340000000000021.000000000000000 552495823354.734000000000000 225423678942.288000000000000 121001614750.848000000000000
X4 remarks0.000000000000000 Continue2.571428571428570 Continue7.915102040816330 Continue
25.686789763524500 Continue92.847753139895400 Continue
307.969049671984000 Continue1073.591674631590000 Continue3645.820284201090000 Continue
12544.963085614500000 Continue42885.628162339400000 Continue
147076.448706914000000 Continue503610.637283945000000 Continue
1725752.882452860000000 Continue5911534.220823330000000 Continue
20253541.086415400000000 Continue69384596.564202000000000 Continue
237708136.494841000000000 Continue814358825.520194000000000 Continue
2789922058.305410000000000 Continue9557980370.082440000000000 Continue
32744719334.029800000000000 Continue112180116200.725000000000000 Continue
Terminate 1.000000000000000x1 x2 x3 x4
2.000000000000000 3.000000000000000 4.000000000000000 5.0000000000000006.000000000000000 7.000000000000000 8.000000000000000 9.000000000000000
10.000000000000000 11.000000000000000 12.000000000000000 13.00000000000000014.000000000000000 15.000000000000000 16.000000000000000 17.000000000000000
K X1 X2 X30.000000000000000 0.000000000000000 0.000000000000000 0.0000000000000001.000000000000000 3.000000000000000 114.000000000000000 76.0000000000000002.000000000000000 27.294117647058800 345.512605042017000 367.7591036414570003.000000000000000 206.034437304334000 4266.968952286800000 3719.8526155560300004.000000000000000 861.779697807615000 34743.770600215700000 31231.9112141369000005.000000000000000 8910.421850341580000 302672.866409518000000 270623.0986937370000006.000000000000000 74739.557899933900000 2606900.476443250000000 2332816.0191014500000007.000000000000000 647561.819063536000000 22492594.922034500000000 20125230.9145843000000008.000000000000000 5582309.426958100000000 194017704.268570000000000 173600341.7653590000000009.000000000000000 48158221.332954600000000 1673629690.740360000000000 1497502233.212330000000000
10.000000000000000 415413733.924887000000000 14436939273.790600000000000 12917646265.839400000000000
xn6.000000000000000
96.000000000000000312.000000000000000416.000000000000000
X40.0000000000000002.1176470588235305.685944966221760
69.788841949697500576.297871043457000
4997.73594930538000043089.001789794200000
371702.8076634900000003206363.517963770000000
27658477.355692700000000238585705.557741000000000
remarksContinueContinueContinueContinueContinueContinueContinueContinueContinueContinueContinue
Given X 0.000000000000000 2.000000000000000 4.000000000000000Linear F(X) 6.000000000000000 12.000000000000000 18.000000000000000
x y x^2 xy0.000000000000000 6.000000000000000 0.000000000000000 0.0000000000000002.000000000000000 12.000000000000000 4.000000000000000 24.0000000000000004.000000000000000 18.000000000000000 16.000000000000000 72.0000000000000006.000000000000000 24.000000000000000 36.000000000000000 144.0000000000000008.000000000000000 30.000000000000000 64.000000000000000 240.000000000000000
10.000000000000000 36.000000000000000 100.000000000000000 360.00000000000000012.000000000000000 42.000000000000000 144.000000000000000 504.00000000000000014.000000000000000 48.000000000000000 196.000000000000000 672.00000000000000016.000000000000000 54.000000000000000 256.000000000000000 864.00000000000000018.000000000000000 60.000000000000000 324.000000000000000 1080.000000000000000
sum: 90.000000000000000 330.000000000000000 1140.000000000000000 3960.000000000000000
Given X 0.000000000000000 2.000000000000000 4.000000000000000F(X) 12.000000000000000 13.000000000000000 15.000000000000000
Polynomialx y x^2 x^3
0.000000000000000 12.000000000000000 0.000000000000000 0.0000000000000002.000000000000000 13.000000000000000 4.000000000000000 8.0000000000000004.000000000000000 15.000000000000000 16.000000000000000 64.0000000000000006.000000000000000 19.000000000000000 36.000000000000000 216.0000000000000008.000000000000000 18.000000000000000 64.000000000000000 512.000000000000000
10.000000000000000 25.000000000000000 100.000000000000000 1000.00000000000000012.000000000000000 40.000000000000000 144.000000000000000 1728.00000000000000014.000000000000000 32.000000000000000 196.000000000000000 2744.00000000000000016.000000000000000 50.000000000000000 256.000000000000000 4096.00000000000000018.000000000000000 55.000000000000000 324.000000000000000 5832.000000000000000
sum: 90.000000000000000 279.000000000000000 1140.000000000000000 16200.000000000000000
a0 12.054545454545300 10.000000000000000a1 0.177272727272726 90.000000000000000a2 0.125000000000000 1140.000000000000000Ym 50.727272727272700
279.0000000000000003312.000000000000000
47280.000000000000000
6.000000000000000 8.000000000000000 10.000000000000000 12.00000000000000024.000000000000000 30.000000000000000 36.000000000000000 42.000000000000000
ym ei^2 y-ymean15.714285714285700 471.510204081633000 49.0000000000000006.285714285714290 334.367346938776000 43.0000000000000003.142857142857140 220.734693877551000 37.000000000000000
12.571428571428600 130.612244897959000 31.00000000000000022.000000000000000 64.000000000000100 25.00000000000000031.428571428571400 20.897959183673500 19.00000000000000040.857142857142900 1.306122448979620 13.00000000000000050.285714285714300 5.224489795918330 7.00000000000000059.714285714285700 32.653061224489700 1.00000000000000069.142857142857100 83.591836734693800 5.000000000000000
6.000000000000000 8.000000000000000 10.000000000000000 12.00000000000000019.000000000000000 18.000000000000000 25.000000000000000 40.000000000000000
x^4 xy x^2y ym0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000
16.000000000000000 26.000000000000000 52.000000000000000 48.000000000000000256.000000000000000 60.000000000000000 240.000000000000000 192.000000000000000
1296.000000000000000 114.000000000000000 684.000000000000000 432.0000000000000004096.000000000000000 144.000000000000000 1152.000000000000000 768.000000000000000
10000.000000000000000 250.000000000000000 2500.000000000000000 1200.00000000000000020736.000000000000000 480.000000000000000 5760.000000000000000 1728.00000000000000038416.000000000000000 448.000000000000000 6272.000000000000000 2352.00000000000000065536.000000000000000 800.000000000000000 12800.000000000000000 3072.000000000000000
104976.000000000000000 990.000000000000000 17820.000000000000000 3888.000000000000000245328.000000000000000 3312.000000000000000 47280.000000000000000 97200.000000000000000
90.000000000000000 1140.000000000000000 10.0000000000000001140.000000000000000 16200.000000000000000 90.000000000000000
16200.000000000000000 245328.000000000000000 1140.000000000000000
90.000000000000000 1140.000000000000000 10.0000000000000001140.000000000000000 16200.000000000000000 90.000000000000000
16200.000000000000000 245328.000000000000000 1140.000000000000000
14.000000000000000 16.000000000000000 18.00000000000000048.000000000000000 54.000000000000000 60.000000000000000
a1 4.714285714285710ymean 55.000000000000000xmean 15.000000000000000
a0 15.714285714285700
14.000000000000000 16.000000000000000 18.00000000000000032.000000000000000 50.000000000000000 55.000000000000000
ei12.00000000000000035.000000000000000
177.000000000000000413.000000000000000750.000000000000000
1175.0000000000000001688.0000000000000002320.0000000000000003022.0000000000000003833.000000000000000
96921.000000000000000
279.000000000000000 1140.0000000000000003312.000000000000000 16200.000000000000000
47280.000000000000000 245328.000000000000000
90.000000000000000 279.0000000000000001140.000000000000000 3312.000000000000000
16200.000000000000000 47280.000000000000000
Data Pointsx 1.000000000000000 2.000000000000000 3.000000000000000 4.000000000000000 5.000000000000000
f(x) 8.000000000000000 2.000000000000000 9.000000000000000 6.000000000000000 12.000000000000000
Lo(x)f(xo)x4 x3 x2 x k M.factor
0.333333333333333 4.666666666666670 23.666666666666700 51.333333333333300 40.000000000000000 0.333333333333333
L1(x)f(x1)x4 x3 x2 x k M.factor
0.333333333333333 4.333333333333330 19.666666666666700 35.666666666666700 20.000000000000000 0.333333333333333
L2(x)f(x2)x4 x3 x2 x k M.factor
2.250000000000000 27.000000000000000 110.250000000000000 175.500000000000000 90.000000000000000 2.250000000000000
L3(x)f(x3)x4 x3 x2 x k M.factor
1.000000000000000 11.000000000000000 41.000000000000000 61.000000000000000 30.000000000000000 1.000000000000000
L4(x)f(x4)x4 x3 x2 x k M.factor
0.500000000000000 5.000000000000000 17.500000000000000 25.000000000000000 12.000000000000000 0.500000000000000
fn(x)x4 x3 x2 x k
1.750000000000000 21.333333333333300 90.750000000000000 ### 92.000000000000000
xi f(xi) delta'f[x] delta''f[x] delta'''f[x] delta''''f[x]2.000000000000000 4.0000000000000004.000000000000000 5.000000000000000 0.5000000000000006.000000000000000 6.000000000000000 0.500000000000000 0.0000000000000008.000000000000000 7.000000000000000 0.500000000000000 0.000000000000000 0.000000000000000
10.000000000000000 8.000000000000000 0.500000000000000 0.000000000000000 0.000000000000000 0.00000000000000012.000000000000000 10.000000000000000 1.000000000000000 0.125000000000000 0.020833333333333 0.002604166666667
delta'''''f[x]
0.054427083333333
bo b1 b2 b3 b4 b54.000000000000000 1.000000000000000 0.125000000000000 0.020833333333333 0.002604166666667 0.054427083333333
n = 16.000000000000000 Function: f(x)= 6x^2+15x-12h = 0.187500000000000
x f(x) f(x) and trapezoidal pattern product2.000000000000000 42.000000000000000 42.0000000000000002.187500000000000 49.523437500000000 99.0468750000000002.375000000000000 57.468750000000000 57.4687500000000002.562500000000000 65.835937500000000 131.6718750000000002.750000000000000 74.625000000000000 74.6250000000000002.937500000000000 83.835937500000000 167.6718750000000003.125000000000000 93.468750000000000 93.4687500000000003.312500000000000 103.523437500000000 207.0468750000000003.500000000000000 114.000000000000000 114.0000000000000003.687500000000000 124.898437500000000 249.7968750000000003.875000000000000 136.218750000000000 136.2187500000000004.062500000000000 147.960937500000000 295.9218750000000004.250000000000000 160.125000000000000 160.1250000000000004.437500000000000 172.710937500000000 345.4218750000000004.625000000000000 185.718750000000000 185.7187500000000004.812500000000000 199.148437500000000 398.2968750000000005.000000000000000 213.000000000000000 213.000000000000000
∑f(x)s 2971.500000000000000I = 278.578125000000000
Romberg Integrationk n h I(h) k = 2 k = 3
1.000000000000000 1.000000000000000 3.000000000000000 835.734375000000000 278.578125000000000 119.3906250000000002.000000000000000 2.000000000000000 1.500000000000000 417.867187500000000 139.289062500000000 59.6953125000000003.000000000000000 4.000000000000000 0.750000000000000 208.933593750000000 69.644531250000000 29.8476562500000004.000000000000000 8.000000000000000 0.375000000000000 104.466796875000000 34.8222656250000005.000000000000000 16.000000000000000 0.187500000000000 52.233398437500000
f(x)= 6x^2+15x-12 a = 2.000000000000000b = 5.000000000000000
f(x) and trapezoidal pattern product pattern42.000000000000000 1.00000000000000099.046875000000000 2.00000000000000057.468750000000000 1.000000000000000
131.671875000000000 2.00000000000000074.625000000000000 1.000000000000000
167.671875000000000 2.00000000000000093.468750000000000 1.000000000000000
207.046875000000000 2.000000000000000114.000000000000000 1.000000000000000249.796875000000000 2.000000000000000136.218750000000000 1.000000000000000295.921875000000000 2.000000000000000160.125000000000000 1.000000000000000345.421875000000000 2.000000000000000185.718750000000000 1.000000000000000398.296875000000000 2.000000000000000213.000000000000000 1.000000000000000
2971.500000000000000
k = 4 k = 555.715625000000000 26.95917338709680027.857812500000000
n = 16.000000000000000 Function: f(x)= 6x^2+15x-12h = 0.187500000000000
x f(x) f(x) and trapezoidal pattern product pattern2.000000000000000 42.000000000000000 42.000000000000000 1.0000000000000002.187500000000000 49.523437500000000 198.093750000000000 4.0000000000000002.375000000000000 57.468750000000000 114.937500000000000 2.0000000000000002.562500000000000 65.835937500000000 263.343750000000000 4.0000000000000002.750000000000000 74.625000000000000 149.250000000000000 2.0000000000000002.937500000000000 83.835937500000000 335.343750000000000 4.0000000000000003.125000000000000 93.468750000000000 186.937500000000000 2.0000000000000003.312500000000000 103.523437500000000 414.093750000000000 4.0000000000000003.500000000000000 114.000000000000000 228.000000000000000 2.0000000000000003.687500000000000 124.898437500000000 499.593750000000000 4.0000000000000003.875000000000000 136.218750000000000 272.437500000000000 2.0000000000000004.062500000000000 147.960937500000000 591.843750000000000 4.0000000000000004.250000000000000 160.125000000000000 320.250000000000000 2.0000000000000004.437500000000000 172.710937500000000 690.843750000000000 4.0000000000000004.625000000000000 185.718750000000000 371.437500000000000 2.0000000000000004.812500000000000 199.148437500000000 796.593750000000000 4.0000000000000005.000000000000000 213.000000000000000 213.000000000000000 1.000000000000000
∑f(x)s 5688.000000000000000I = 355.500000000000000
a = 2.000000000000000b = 5.000000000000000
Romberg Integrationk n h I(h) k = 2 k = 3
1.000000000000000 1.000000000000000 3.000000000000000 1066.500000000000000 355.500000000000000 152.3571428571430002.000000000000000 2.000000000000000 1.500000000000000 533.250000000000000 177.750000000000000 76.1785714285714003.000000000000000 4.000000000000000 0.750000000000000 266.625000000000000 88.875000000000000 38.0892857142857004.000000000000000 8.000000000000000 0.375000000000000 133.312500000000000 44.4375000000000005.000000000000000 16.000000000000000 0.187500000000000 66.656250000000000
k = 4 k = 571.100000000000000 34.40322580645160035.550000000000000
n = 12.000000000000000 Function: f(x)= 6x^2+15x-12 a =h = 0.250000000000000 b =
x f(x) f(x) and trapezoidal pattern product pattern2.000000000000000 42.000000000000000 42.000000000000000 1.0000000000000002.250000000000000 52.125000000000000 156.375000000000000 3.0000000000000002.500000000000000 63.000000000000000 189.000000000000000 3.0000000000000002.750000000000000 74.625000000000000 149.250000000000000 2.0000000000000003.000000000000000 87.000000000000000 261.000000000000000 3.0000000000000003.250000000000000 100.125000000000000 300.375000000000000 3.0000000000000003.500000000000000 114.000000000000000 228.000000000000000 2.0000000000000003.750000000000000 128.625000000000000 385.875000000000000 3.0000000000000004.000000000000000 144.000000000000000 432.000000000000000 3.0000000000000004.250000000000000 160.125000000000000 320.250000000000000 2.0000000000000004.500000000000000 177.000000000000000 531.000000000000000 3.0000000000000004.750000000000000 194.625000000000000 583.875000000000000 3.0000000000000005.000000000000000 213.000000000000000 426.000000000000000 2.0000000000000005.250000000000000 232.125000000000000 696.375000000000000 3.0000000000000005.500000000000000 252.000000000000000 756.000000000000000 3.0000000000000005.750000000000000 272.625000000000000 545.250000000000000 2.0000000000000006.000000000000000 294.000000000000000 294.000000000000000 1.000000000000000
∑f(x)s 4701.375000000000000I = 440.753906250000000
2.0000000000000005.000000000000000
Romberg Integrationk n h I(h) k = 2 k = 3
1.000000000000000 1.000000000000000 3.000000000000000 1322.261718750000000 440.753906250000000 188.8945312500000002.000000000000000 2.000000000000000 1.500000000000000 661.130859375000000 220.376953125000000 94.4472656250000003.000000000000000 4.000000000000000 0.750000000000000 330.565429687500000 110.188476562500000 47.2236328125000004.000000000000000 8.000000000000000 0.375000000000000 165.282714843750000 55.0942382812500005.000000000000000 16.000000000000000 0.187500000000000 82.641357421875000
k = 4 k = 588.150781250000000 42.65360383064520044.075390625000000
Forward Diff Backward DiffXi f(Xi) Xi+1 f(Xi+1) f'(Xi) h Xi f(Xi) Xi-1 f(Xi-1) f'(Xi)
1 0.5 5.375 1.5 29.125 23.75 1 0.5 5.375 -0.5 -9.375 14.750.5 1 15 1.5 16.125 2.25 0.5 1 15 0.5 5.375 19.25
0.25 1.5 29.125 1.75 25.57813 -14.1875 0.25 1.5 29.125 1.25 21.35938 31.06250.125 2 50 2.125 43.53711 -51.70313 0.125 2 50 1.875 44.02539 47.79688
Richardson's Extrapolation Richardson's Extrapolationk h D(h) k = 2 k = 3 k = 4 k h D(h) k = 2 k = 3 k = 41 1 23.75 -4.916667 -21.77381 -73.8246 1 1 14.75 20.75 37.03571 57.264292 0.5 2.25 -19.66667 -70.57143 2 0.5 19.25 35 563 0.25 -14.1875 -64.20833 3 0.25 31.0625 53.3754 0.125 -51.70313 4 0.125 47.79688
F(x) = 3x^3+14x-2
Center Diffh Xi-1 Xi+1 f(Xi-1) f(Xi+1) f'(Xi) Xi1 -0.5 1.5 -9.375 29.125 19.25 0.5
0.5 0.5 1.5 5.375 29.125 23.75 10.25 1.25 1.75 21.35938 38.57813 34.4375 1.5
0.125 1.875 2.125 44.02539 56.53711 50.04688 2
Richardson's Extrapolationk h D(h) k = 2 k = 3 k = 41 1 19.25 25.25 39.82143 58.907142 0.5 23.75 38 57.714293 0.25 34.4375 55.254 0.125 50.04688