On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots - Archive ouverte HAL
Journal Articles Electronic Transactions on Numerical Analysis Year : 2022

On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots

Thomas R. Cameron
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Abstract

In this article, we use the complex compensated Horner's method to derive a compensated Ehrlich-Aberth method for the accurate computation of all roots of a polynomial. In particular, under suitable conditions, we prove that the limiting accuracy for the compensated Ehrlich-Aberth iterations is as accurate as if computed in twice the working precision and then rounded into the working precision. Moreover, we derive a running error bound for the complex compensated Horner's and use it to form robust stopping criteria for the compensated Ehrlich-Aberth iterations. Finally, extensive numerical experiments illustrate that the backward and forward errors of the root approximations computed via the compensated Ehrlich-Aberth method are similar to those obtained with a quadruple precision implementation of the Ehrlich-Aberth method with a significant speed-up in terms of the computation time.
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Dates and versions

hal-03335604 , version 1 (06-09-2021)

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Cite

Thomas R. Cameron, Stef Graillat. On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots. Electronic Transactions on Numerical Analysis, 2022, 55, pp.401-423. ⟨10.1553/etna_vol55s401⟩. ⟨hal-03335604⟩
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