Efficient path tracking methods

Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particu...

Full description

Saved in:
Bibliographic Details
Published inNumerical algorithms Vol. 58; no. 4; pp. 451 - 459
Main Authors Bates, Daniel J., Hauenstein, Jonathan D., Sommese, Andrew J.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2011
Springer Nature B.V
Subjects
Algebra
Algorithms
Computer Science
Numeric Computing
Numerical Analysis
Original Paper
Path tracking
Polynomials
Predictor-corrector methods
Runge-Kutta method
Software
Theory of Computation
65L06
Polynomial systems
Path tracking
Euler’s method
Precision
65H20
Ordinary differential equations
Homotopy continuation
65E05
65H10
Runge-Kutta methods
Adaptive precision
Numerical algebraic geometry
Online AccessGet full text
ISSN1017-1398
1572-9265
DOI10.1007/s11075-011-9463-8

Cover

More Information
Summary:Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particularly in the specialized algebraic setting of solving polynomial systems. In this article, the effects of the choice of predictor method on the performance of a tracker is analyzed, and details for using Runge-Kutta methods in conjunction with adaptive precision are provided. These methods have been implemented in the Bertini software package, and several examples are described.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-011-9463-8