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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.


Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division
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by G. W. Stewart PDF
Math. Comp. 25 (1971), 135-139 Request permission


An analysis is given of the role of rounding errors in the synthetic division algorithm for computing the coefficients of the polynomial $g(z) = f(z + s)$ from the coefficients of the polynomial f. It is shown that if $|z + s| \cong |z| + |s|$ then the value of the computed polynomial ${g^\ast }(z)$ differs from $g(z)$ by no more than a bound on the error made in computing $f(z + s)$ with rounding error. It may be concluded that well-conditioned zeros of f lying near s will not be seriously disturbed by the shift.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 135-139
  • MSC: Primary 65H05
  • DOI:
  • MathSciNet review: 0292333