# Spectral approximation of convolution operator

Xu, Kuan, Loureiro, Ana F. (2018) Spectral approximation of convolution operator. SIAM Journal on Scientific Computing, 40 (4). A2336-A2355. ISSN 1064-8275. E-ISSN 1095-7197. (doi:10.1137/17M1149249)

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## Abstract

We develop a unified framework for constructing matrix approximations for the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials on [?1, 1]. The numerically stable algorithms we propose exploit recurrence relations and symmetric properties satisfied by the entries of these convolution matrices. Laguerrebased convolution matrices that approximate Volterra convolution operator defined by functions on [0, ?] are also discussed for the sake of completeness.

Item Type: Article 10.1137/17M1149249 convolution, Volterra convolution integral, operator approximation, orthogonal polynomials, Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, ultraspherical polynomials, Jacobi polynomials, Laguerre polynomials, spectral methods Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics Ana F. Loureiro 10 Nov 2017 11:37 UTC 15 Jan 2020 15:56 UTC https://kar.kent.ac.uk/id/eprint/64340 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4137-8822