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Error Analysis for Polynomial Evaluation

A. C. R. Newbery
Mathematics of Computation
Vol. 28, No. 127 (Jul., 1974), pp. 789-793
DOI: 10.2307/2005700
Stable URL: http://www.jstor.org/stable/2005700
Page Count: 5
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Error Analysis for Polynomial Evaluation
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Abstract

A floating-point error analysis is given for the evaluation of a real polynomial at a real argument by Horner's scheme. A computable error bound is derived. It is observed that when a polynomial has coefficients of constant sign or of strictly alternating sign, one cannot expect better accuracy by reformulating the problem in terms of Chebyshev polynomials.

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