On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

https://doi.org/10.1137/0202007

Abstract

We present algorithms which use only $O(\sqrt n )$ nonscalar multiplications (i.e. multiplications involving “x” on both sides) to evaluate polynomials of degree n, and proofs that at least $\sqrt n $ are required. These results have practical application in the evaluation of matrix polynomials with scalar coefficients, since the “matrix $ \times $ matrix” multiplications are relatively expensive, and also in determining how many multiplications are needed for polynomials with rational coefficients, since multiplications by integers can in principle be replaced by several additions.

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Volume 2, Issue 1| 1973

SIAM Journal on Computing

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Submitted:03 December 1971
Published online:13 July 2006

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Article DOI:10.1137/0202007

Article page range:pp. 60-66

ISSN (print):0097-5397

ISSN (online):1095-7111

Publisher:Society for Industrial and Applied Mathematics

On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

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