Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911813664243712 |
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| author | Gutleb, Timon S. Olver, Sheehan Slevinsky, Richard Mikael |
| author_facet | Gutleb, Timon S. Olver, Sheehan Slevinsky, Richard Mikael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations Gutleb, Timon S. Olver, Sheehan Slevinsky, Richard Mikael Numerical Analysis 33C45, 33C47, 33C50, 42C05, 15A23 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. |
| title | Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations |
| topic | Numerical Analysis 33C45, 33C47, 33C50, 42C05, 15A23 |
| url | https://arxiv.org/abs/2302.08448 |