Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division
Abstract: An analysis is given of the role of rounding errors in the synthetic division algorithm for computing the coefficients of the polynomial from the coefficients of the polynomial f. It is shown that if then the value of the computed polynomial differs from by no more than a bound on the error made in computing 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