Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65H05

Retrieve articles in all journals with MSC: 65H05

Additional Information

Keywords: Rounding error, shifting algorithm, synthetic division, zeros of polynomials
Article copyright: © Copyright 1971 American Mathematical Society