Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
arxiv(2023)
摘要
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.
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