A fast Björck-Pereyra-like algorithm for solving quasiseparable- Hessenberg-Vandermonde systems
نویسندگان
چکیده
In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde VR(x) = [rj−1(xi)] matrix with polynomials R related to a quasiseparable matrix. The result is a generalization of the well-known Björck-Pereyra algorithm for classical Vandermonde systems. As will be shown, many important systems of polynomials are related to quasiseparable matrices in this way, and thus this result also generalizes the algorithms derived in [RO91] for Chebyshev polynomials, [H90] for real orthogonal polynomials, and [BEGKO07] for Szegö polynomials. Numerical experiments are presented comparing the algorithm to standard structure-ignoring methods.
منابع مشابه
A Fast Björck-Pereyra-Type Algorithm for Solving Hessenberg-Quasiseparable-Vandermonde Systems
In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde matrix VR(x) = [rj−1(xi)] with polynomials {rk(x)} related to a Hessenberg quasiseparable matrix. The result generalizes the well-known Björck-Pereyra algorithm for classical Vandermonde systems involving monomials. It also generalizes the algorithms of [RO91] for VR...
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