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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