Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations

02/16/2023

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by   Timon S. Gutleb, et al.

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University of Oxford

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University of Manitoba

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Imperial College London

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We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via infinite-dimensional banded matrix factorizations and may be used to compute the modified Jacobi matrices all in linear complexity with respect to the truncation degree. A family of orthogonal polynomials with modified classical weights is constructed that support banded differentiation matrices, enabling sparse spectral methods with modified classical orthogonal polynomials.