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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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 $ \vert z + s\vert \cong \vert z\vert + \vert s\vert$ 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

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0292333-7
PII: S 0025-5718(1971)0292333-7
Keywords: Rounding error, shifting algorithm, synthetic division, zeros of polynomials
Article copyright: © Copyright 1971 American Mathematical Society