Multiprecision path tracking

Details Multiprecision path tracking Multiprecision path tracking

2006-05-03

arxiv.org/abs/math/0605105v1

Mathematics

Numerical Analysis

Scientific paper

A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost than would be incurred by raising precision across the board. We develop simple rules for adjusting precision and show how to integrate these into an algorithm that also adaptively adjusts the step size. The behavior of the method is illustrated on several examples arising as homotopies for solving systems of polynomial equations.

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