Spectral approximation of convolution operator
Provides numerically stable algorithms for approximating convolution operators, benefiting computational mathematics and numerical analysis.
The paper develops a unified framework for constructing stable matrix approximations to Volterra convolution operators using orthogonal polynomials, with algorithms exploiting recurrence and symmetry properties.
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 operator defined by functions on $[0, \infty]$ are also discussed for the sake of completeness.