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Incomplete Gröbner basis as a preconditioner for polynomial systems

✍ Scribed by Yang Sun; Yu-Hui Tao; Feng-Shan Bai

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
446 KB
Volume
226
Category
Article
ISSN
0377-0427

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✦ Synopsis

Precondition 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.

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