Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
Numerical Analysis
2024-03-27 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2302.08448,
title = {Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations},
author = {Timon S. Gutleb and Sheehan Olver and Richard Mikael Slevinsky},
journal= {arXiv preprint arXiv:2302.08448},
year = {2024}
}