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Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems

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arxiv 1212.4699 v1 pith:VUK4XINB submitted 2012-12-19 math.NA cs.NA

Nan Li , Lihong Zhi This is my paper
classification math.NAcs.NA
keywords singularboundssolutionssystemsalgorithmerrorisolatedpolynomial
verification ladder T0 review T1 audit T2 compute T3 formal
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In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly perturbed system is guaranteed to possess an isolated singular solution within the computed bounds. Our new verification method is based on deflation techniques using smoothing parameters. We demonstrate the performance of the algorithm for systems with singular solutions of multiplicity up to hundreds.

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