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June 2007 Tighter Bounds of Errors of Numerical Roots
Tateaki Sasaki
Japan J. Indust. Appl. Math. 24(2): 219-226 (June 2007).

Abstract

Let $P(z)$ be a monic univariate polynomial over $\mathbf{C}$, of degree $n$ and having roots $\zeta_1,\ldots,\zeta_n$. Given approximate roots $z_1,\ldots,z_n$, with $\zeta_i \simeq z_i$ ($i=1,\ldots,n$), we derive a very tight upper bound of $|\zeta_i - z_i|$, by assuming that $\zeta_i$ has no close root. The bound formula has a similarity with Smale's and Smith's formulas. We also derive a lower bound of $|\zeta_i - z_i|$ and a lower bound of $\min\{|\zeta_j - z_i|\mid j \neq i\}$.

Citation

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Tateaki Sasaki. "Tighter Bounds of Errors of Numerical Roots." Japan J. Indust. Appl. Math. 24 (2) 219 - 226, June 2007.

Information

Published: June 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1133.65027
MathSciNet: MR2338156

Rights: Copyright © 2007 The Japan Society for Industrial and Applied Mathematics

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Vol.24 • No. 2 • June 2007
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