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Generalized Gaussian quadratures appear to have been introduced by Markov late in the 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 an absence of effective numerical schemes for their construction. Recently, a numerical scheme for the design of such quadratures was introduced by Ma et al.; numerical results presented in their paper indicate that such quadratures dramatically reduce the computational cost of the evaluation of integrals under certain conditions. In this paper, we modify their approach, improving the stability of the scheme and extending its range of applicability. The performance of the method is illustrated with several numerical examples.
Yarvin et al. (Thu,) studied this question.