Upload File

overview: numerically solving systems of polynomial equations · overview: numerically solving...

  • Home
  • Documents
  • Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
73
Overview: Numerically solving systems of polynomial equations Jonathan Hauenstein Summer School on Numerical Computing in Algebraic Geometry August 13, 2018

Upload: others

Post on 19-Mar-2020

9 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

Overview: Numerically solving systems of polynomial equations

Jonathan HauensteinSummer School on Numerical Computing in Algebraic Geometry

August 13, 2018

Page 2: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 3: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 4: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 5: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 6: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 7: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

EarlyHistory of Solving

Page 8: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 9: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 10: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 11: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 12: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 13: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 14: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 15: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 16: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 17: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 18: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 19: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 20: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 21: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 22: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 23: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 24: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 25: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 26: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 27: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 28: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 29: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 30: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 31: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 32: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 33: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

Late 20th

Century1970s – 1990s

Page 34: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 35: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 36: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 37: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 38: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 39: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 40: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 41: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 42: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 43: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 44: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 45: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 46: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 47: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 48: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 49: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 50: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 51: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 52: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 53: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

Early 21st

Century

Page 54: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 55: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 56: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 57: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 58: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 59: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 60: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 61: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 62: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 63: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 64: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 65: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 66: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 67: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 68: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

Future?

Page 69: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 70: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 71: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 72: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing
Page 73: Overview: Numerically solving systems of polynomial equations · Overview: Numerically solving systems of polynomial equations. Jonathan Hauenstein. Summer School on Numerical Computing

7.4 Solving Polynomial Equations

From Solving Polynomial Equations to Groups

Solving Monotone Polynomial Equationsesparza/Talks/tcs08.pdf · Solving Monotone Polynomial Equations Javier Esparza Stefan Kiefer Michael Luttenberger Technische Universität München

Solving Polynomial Systems by Homotopy Continuation

Solving Third Degree Polynomial Equations · 2. An algorithm to beautify the solutions 3. Solving a third degree polynomial equation with 1 real root 4. Solving a third degree polynomial

Solving systems of polynomial inequalities with algebraic ... · Solving systems of polynomial inequalities with algebraic geometry methods Laura Menini, Corrado Possieriyand Antonio

A Consistently Rapid Algorithm for Solving Polynomial Equations

Numerically solving the sound transmission in the intake ...essay.utwente.nl/69274/1/Joost_Maas_Report_2014_UT.pdf · ISVR University of Southampton Internship 2013 Numerically solving

6.4 Factoring and Solving Polynomial Equations. Factor Polynomial Expressions In the previous lesson, you factored various polynomial expressions. Such

On the Communication Complexity of Solving a Polynomial

Solving Polynomial Equations - Williams College · Solving Polynomial Equations Part III. ... equation by means of continued fractions, ... and partial differential equations and

Polynomial System Solving in Maple 16 › view.aspx?SF=132208 › Polynomial... · Polynomial System Solving in Maple 16 Computing and manipulating the real solutions of a polynomial

Chapter 9 Solving Second order differential equations numerically, 2

Solving Polynomial Equations Applications

Numerically Stable Stochastic Simulation Approaches for ... · Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models ∗ Kenneth Judd, Lilia Maliar

Algebra 2B Name Review (Solving Polynomial Equations and

Finite Element Method For Numerically Solving PDE's

Numerical Computations in Algebraic Geometry Jan Verscheldejan/Talks/numalgmrc.pdf · 2008-06-24 · Outline 1 Numerically Solving Polynomial Systems 2 Zero Dimensional Solving homotopy

Solving Polynomial Equations - USM...logo1 Introduction Quadratic Equations Cubic Equations Quartic Equations Solving Polynomial Equations Bernd Schroder¨ Bernd Schroder¨ Louisiana

GRAPHING AND SOLVING POLYNOMIAL EQUATIONS · 2020-04-22 · GRAPHING AND SOLVING POLYNOMIAL EQUATIONS Unit Overview In this unit you will graph polynomial functions and describe end

Solving Systems of Polynomial Equations Bernd Sturmfels

Example 1: Solving a Polynomial Equationmrshuntsmathsite.weebly.com/uploads/3/8/1/3/... · 1 February 21, 2017 5-3 Solving Polynomial Equations: Example 1: Solving a Polynomial Equation

Solving equations - GHS Maths Methods Unit 3 & 4ghsmethods12.weebly.com/.../4/...solving_equations.pdf · Solving polynomial equations Polynomial equations, whether they be quadratics,

1 5.4 Polynomial and Rational Inequalities In this section, we will study the following topics: Solving polynomial inequalities Solving rational inequalities

Solving partial differential equations numerically on ...lindblom/Publications/93_JCompPhys.243.15… · Title: Solving partial differential equations numerically on manifolds with

CHAPTER 9 Solving Quadratic Equations - Big Ideas Learning€¦ · CHAPTER 9 Solving Quadratic Equations 9.1 Solving Polynomial Equations in Factored Form ... 9.1 Solving Polynomial

Solving Systems of Polynomial Equations Bernd Sturmfelsbernd/cbms.pdf · Solving Systems of Polynomial Equations Bernd Sturmfels ... developments in symbolic algebra and numerical

7.4 Solving Polynomial Equations in Factored Form · Section 7.4 Solving Polynomial Equations in Factored Form 377 ... 380 Chapter 7 Polynomial Equations and Factoring Solving Equations

Solving Polynomial Systems Equation by Equation

Solving Polynomial Systems

Solving Polynomial Systems - homepages.math.uic.eduhomepages.math.uic.edu/~adrovic/siamag2013.pdf · Solving Polynomial Systems in Noether Position ... tropical version of Backelin’s

Solving systems of polynomial equations and minimization of ...perso.uclouvain.be/francois.glineur/oldwww/Papers/CESAME06.pdf · Solving systems of polynomial equations and minimization

Solving Polynomial Equation Systems I

Solving Polynomial Equation Systems I - The Library of ...catdir.loc.gov/catdir/samples/cam033/2001043132.pdf · Solving Polynomial Equation Systems I ... whose iterative application

Certificates in Numerical Algebraic Geometry Jan Verscheldejan/Talks/certificates.pdf · about numerically solving polynomial systems two examples from mechanism design problem statement: