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
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.References
- J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 135-139
- MSC: Primary 65H05
- DOI: https://doi.org/10.1090/S0025-5718-1971-0292333-7
- MathSciNet review: 0292333