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Fast and accurate evaluation of dual Bernstein polynomials

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Abstract

Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis, and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of these polynomials and their linear combinations. New simple recurrence relations of low order satisfied by dual Bernstein polynomials are given. In particular, a first-order non-homogeneous recurrence relation linking dual Bernstein and shifted Jacobi orthogonal polynomials has been obtained. When used properly, it allows to propose fast and numerically efficient algorithms for evaluating all n + 1 dual Bernstein polynomials of degree n with O(n) computational complexity.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, ul. F. Joliot-Curie 15, 50-383, Wrocław, Poland

    Filip Chudy & Paweł Woźny

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  1. Filip Chudy
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  2. Paweł Woźny
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Correspondence to Paweł Woźny.

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Chudy, F., Woźny, P. Fast and accurate evaluation of dual Bernstein polynomials. Numer Algor 87, 1001–1015 (2021). https://doi.org/10.1007/s11075-020-00996-5

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