Newton's method with deflation for isolated singularities of polynomial systems

Details Newton's method with deflation for isolated singularities of polynomial systems Newton's method with deflation for isolated singularities of polynomial systems

2004-08-30

arxiv.org/abs/math/0408419v2

Mathematics

Numerical Analysis

15 pages; preliminary version presented as poster at ISSAC 2004, 6 July 2004, conjecture on number of deflations is proven

Scientific paper

We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution as a regular root. Using standard bases, a tool for the symbolic computation of multiplicities, we show that the number of deflation stages is bounded by the multiplicity of the isolated root. Our implementation performs well on a large class of applications.

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