Year: 2018
Type: article
Abstract: We develop a unified framework for constructing matrix approximations to 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. Laguerre-based convolution matrices that approximate Volterra convolution operators defined by functions on $[0, \infty)$ are also discussed for the sake of completeness.
DOI: 10.1137/17m1149249
Authors: Kuan Xu, Ana F. Loureiro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5578772150
OpenAlex ID: W2773734884