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A Matlab package computing polynomial roots and multiplicities by Zhonggang Zeng is a Computer Science article available to read on EtoBox.

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MULTROOT is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with high multiplicities, using standard machine precision. As a blackbox-type software, MULTROOT requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, as well as the pejorative condition number.There are two common limitations for standard numerical root-finding software when multiple roots are present. Namely, those methods suffer from severe loss of accuracy and lack the capacity of multiplicity identification. Symbolic polynomial factorization requires __exact__ rational coefficients. In contrast, the most significant features of MULTROOT are the multiplicity identification capability and the remarkable accuracy on multiple roots without using the multiprecision arithmetic, even if the polynomial coefficients are inexact.There is a so-called "attainable accuracy" for conventional root-finders: the attainable number of corrected digits of a computed root is limited by the data/machine precision divided by the multiplicity. For roots with high multiplicities, this accuracy barrier sugge

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Author

Zhonggang Zeng

Publisher

ACM

Published

2004

Language

EN

Field

Computer Science (Physical Sciences)