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
DOI:
https://doi.org/10.1090/S0025-5718-1971-0292333-7
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.
- J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
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Keywords:
Rounding error,
shifting algorithm,
synthetic division,
zeros of polynomials
Article copyright:
© Copyright 1971
American Mathematical Society