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

Anton Leykin·Jan Verschelde·Ailing Zhao
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Abstract

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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Anton Leykin, Jan Verschelde, Ailing Zhao. 2004-10-13. Newton's method with deflation for isolated singularities of polynomial systems. https://arxiv.org/abs/math/0408419

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