Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials

Details Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials

2003-06-02

arxiv.org/abs/cs/0306015v1

Computer Science

Numerical Analysis

13 pages, no figures

Scientific paper

There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given polynomial using Rouche's theorem from complex analysis. We compute the error bounds using non-linear optimization. Our bounds are scalable in the sense that we compute sharper error bounds for better approximations of zeros. We use high precision computations using the LEDA/real floating-point filter for computing our bounds robustly.

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