Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's TheoremsError Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems

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 Author Smith, Brian T. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1970 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Given $\textit{N}$ approximations to the zeros of an $\textit{N}th-degree$ polynomial, $\textit{N}$ circular regions in the complex $\textit{z}-plane$ are determined whose union contains all the zeros, and each connected component of this union consisting of $\textit{K}$ such circular regions contains exactly $\textit{K}$ zeros. The bounds for the zeros provided by these circular regions are not excessively pessimistic; that is, whenever the approximations are sufficiently well separated and sufficiently close to the zeros of this polynomial, the radii of these circular regions are shown to overestimate the errors by at most a modest factor simply related to the configuration of the approximations. A few numerical examples are included. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1970-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 17 Issue Number 4 Page Count 14 Starting Page 661 Ending Page 674

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Source: ACM Digital Library