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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A numerical accuracy consideration in polynomial deflation
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by C. J. O’Neill and T. Downs PDF
Math. Comp. 32 (1978), 1144-1146 Request permission

Abstract:

In a recent paper, Peters and Wilkinson described a composite deflation method which provides an accurate technique for the determination of the roots of a polynomial where these roots are widely spaced. By examples involving deflation by linear factors they demonstrated that the method was much more accurate than forward or backward deflation. In addition, they stated that the method could also be used when deflating by a quadratic factor or a polynomial of higher degree. In this short note it is shown that composite deflation by quadratic factors can lead to severe rounding error where two successive deflations by linear factors produce a perfectly accurate result.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 1144-1146
  • MSC: Primary 65H05; Secondary 65G05
  • DOI: https://doi.org/10.1090/S0025-5718-1978-0502003-1
  • MathSciNet review: 502003