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Tighter bounds of errors of numerical roots

  • Tateaki SasakiEmail author
Article
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Abstract

LetP(z) be a monic univariate polynomial overC, of degreen and having roots ζ1,..., ζ n . Given approximate rootsz 1,...,z n, with ζ i z i (i = 1,...,n), we derive a very tight upper bound of ¦ζ i z i¦, by assuming that ζ 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 ¦ζ i z i¦ and a lower bound of min{ζ j z i¦ ¦ji}.

Keywords

Error Bound Tight Bound Numerical Root Approximate Root Close Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© JJIAM Publishing Committee 2007

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TsukubaIbarakiJapan

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