On the Multivariate Horner Scheme

Authors:
J. M. Peña
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 6

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Abstract

We present an efficient version of the Horner scheme for the evaluation of multivariate polynomials and study its stability properties. In particular, we show that the backward error of evaluation is bounded by a quantity that is linear in the total degree of the polynomial, which itself is usually significantly smaller than the number of operations involved in the evaluation process. Moreover, we show that the same type of estimates holds also for the forward error, provided that the polynomial basis is chosen suitably.