Using Numerical Insights to Improve Symbolic Computations

Abstract

Numerical algebraic geometry provides a toolbox of numerical methods for performing computations involving systems of polynomial equations. Even though some of the computations which are performed on a computer using floating-point arithmetic are not certified, they can often be made very reliable using adaptive precision computations. Moreover, there is a wealth of information regarding the original problem which can be extracted from various numerical computation that can be used to improve subsequent symbolic computations to certify the result. This paper highlights two applications of such hybrid numeric-symbolic methods in algebraic geometry.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2018
Accession Number
AD1121866

Entities

People

  • Jonathan D Hauenstein

Organizations

  • University of Notre Dame

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Algebra
  • Algebraic Geometry
  • Algorithms
  • Arithmetic
  • Coefficients
  • Complex Numbers
  • Computations
  • Computers
  • Elimination
  • Engineering
  • Equations
  • Floating Point Operations
  • Geometry
  • Mathematics
  • New York
  • Numbers
  • Polynomials
  • Precision
  • Topology

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Computer Programming and Software Development.