SPECTRAL APPROXIMATION OF CONVOLUTION OPERATORS

摘要

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,infinity) are also discussed for the sake of completeness.