Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis

Authors:
Manfred Minimair
Affiliations:
Department of Mathematics and Computer Science, Seton Hall University, New Jersey, USA 07079
Venue:
Computer Mathematics
Year:
2008

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Abstract

Division algorithms for univariate polynomials represented with respect to Lagrange and Bernstein basis are developed. These algorithms are obtained by abstracting from the classical polynomial division algorithm for polynomials represented with respect to the usual power basis. It is shown that these algorithms are quadratic in the degrees of their inputs, as in the power basis case.