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Author Watkins, Bruce O. ♦ Henrici, P.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Abstract A method which finds simultaneously all the zeros of a polynomial, developed by H. Rutishauser, has been tested on a number of polynomials with real coefficients. This slowly converging method (the Quotient-Difference (Q-D) algorithm) provides starting values for a Newton or a Bairstow algorithm for more rapid convergence.Necessary and sufficient conditions for the existence of the Q-D scheme are not completely known; however, failure may occur when zeros have equal, or nearly equal magnitudes. Success was achieved, in most of the cases tried, with the failures usually traceable to the equal magnitude difficulty. In some cases, computer roundoff may result in errors which spoil the scheme. Even if the Q-D algorithm does not give all the zeros, it will usually find a majority of them.
Description Affiliation: Univ. of California, Los Angeles, and Technische Hochschule, Zurich, Switzerland (Henrici, P.) || Utah State Univ., Logan (Watkins, Bruce O.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 8
Issue Number 9
Page Count 5
Starting Page 570
Ending Page 574


Source: ACM Digital Library