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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 Iz + sl -l z + Ist then the value of the computed polynomial g*(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.

Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division