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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)


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
DOI/Identification number: 10.1137/17M1149249
Uncontrolled keywords: convolution, Volterra convolution integral, operator approximation, orthogonal polynomials, Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, ultraspherical polynomials, Jacobi polynomials, Laguerre polynomials, spectral methods
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Ana F. Loureiro
Date Deposited: 10 Nov 2017 11:37 UTC
Last Modified: 15 Jan 2020 15:56 UTC
Resource URI: (The current URI for this page, for reference purposes)
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