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Mathematics of Computation

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Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division

Author: G. W. Stewart
Journal: Math. Comp. 25 (1971), 135-139
MSC: Primary 65H05
MathSciNet review: 0292333
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Abstract: 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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Keywords: Rounding error, shifting algorithm, synthetic division, zeros of polynomials
Article copyright: © Copyright 1971 American Mathematical Society