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TitleIncomplete Gröbner basis as a preconditioner for polynomial systems
Author(s) Feng-Shan Bai, Yao Sun, Yu-Hui Tao
TypeArticle in Journal
AbstractPrecondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.
KeywordsIncomplete Gröbner basis (IGB), Homotopy continuation method, Subtraction polynomial ( S -polynomial), Precondition
ISSN0377-0427
URL http://www.sciencedirect.com/science/article/pii/S0377042708002161
LanguageEnglish
JournalJournal of Computational and Applied Mathematics
Volume226
Number1
Pages2 - 9
Year2009
NoteSpecial Issue: The First International Conference on Numerical Algebra and Scientific Computing (NASC06)
Edition0
Translation No
Refereed No
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