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arXiv · 2206.07560

Sobolev-Orthogonal Systems with Tridiagonal Skew-Hermitian Differentiation Matrices

Arieh Iserles·Marcus Webb
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Abstract

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterise such systems completely as appropriately weighed Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev-orthogonal system whose leading N coefficients can be computed in $\mathcal{O}(N \log N)$ operations.

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BibTeXRIS

Arieh Iserles, Marcus Webb. 2022-06-15. Sobolev-Orthogonal Systems with Tridiagonal Skew-Hermitian Differentiation Matrices. https://arxiv.org/abs/2206.07560

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