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Associated Polynomials and Uniform Methods for the Solution of Linear Problems

Traub, Joseph F.

To every polynomial P of degree n we associate a sequence of n-1 polynomials of increasing degree which we call the associated polynomials of P. The associated polynomials depend in a particularly simple way on the coefficients of P. These polynomials have appeared in many guises in the literature, usually related to some particular application and most often going unrecognized. They have been called Horner polynomials and Laguerre polynomials. Often what occurs is not an associated polynomial itself but a number which is an associated polynomial evaluated at a zero of P. The properties of associated polynomials have never been investigated in themselves. We shall try to demonstrate that associated polynomials provide a useful unifying concept. Although many of the results of this paper are new, we shall also present known results in our framework.

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Also Published In

Title
SIAM Review
DOI
https://doi.org/10.1137/1008061

More About This Work

Academic Units
Computer Science
Published Here
October 10, 2013
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