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Solving Finite Algebraic Systems Using Numeric Gröbner Bases and Eigenvalues
Author

Daniel Lichtblau
Organization: Wolfram Research, Inc.
Conference

SCI 2000
Conference location

Orlando, FL
Description

Paper and accompanying talk presented at SCI 2000 (July 2000, Orlando, Florida)

Abstract:

Systems of algebraic equations with finitely many solutions arise in many areas of applied mathematics. Among these are motion planning, robotics, computer-aided design, and graphics. We will discuss the design and implementation of a hybrid symbolic-numeric method, and a Mathematica implementation thereof, that finds all solutions to an algebraic system. It makes use of numeric Gröbner bases and arbitrary-precision numeric eigenvalue computation. We explain in outline how this works, and give a few examples that demonstrate how this can be useful technology independent of Newton's method local solvers.
Subjects

*Mathematica Technology > Kernel > Numerics
*Mathematics > Algebra > Field and Ring Theory
*Mathematics > Algebra > Linear Algebra
*Mathematics > Algebra > Polynomials
Keywords

algebraic equations, Gröbner basis, eigenvalues, hybrid symbolic-numeric solving
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nsolve_paper.pdf (55.7 KB) - PDF Document
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nsolve_sci2000_talk.pdf (138 KB) - PDF Document
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nsolve_paper.nb (89.7 KB) - Mathematica Notebook
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nsolve_sci2000_talk.nb (28.9 KB) - Mathematica Notebook