Generalized Gaussian Quadratures and Singular Value Decompositions of IntegralOperators

摘要

Generalized Gaussian quadratures appear to have been introduced by Markov late inthe last century, and have been studied in great detail as a part of modern analysis. They have not been widely used as a computational tool, in part due to absence of effective numerical schemes for their construction. Recently, a numerical scheme was introduced for the design of such quadratures; numerical results presented indicate that such quadratures dramatically reduce the computational cost of the evaluation of integrals under certain conditions. In this paper, we modify the approach, improving the stability of the scheme and extending its range of applicability. The performance of the method is illustrated with several numerical examples.