Computing the coefficients of a recurrence formula for numerical integration by moments and modified moments

• Autores: M. Morandi Cecchi, M. Redivo Zaglia
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Nº 1, 1993, pág. 207
• Idioma: inglés
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• Resumen

  • To evaluate the class of integrals ∫1−1e−αxƒ(x) dx, where † and the function f(x) is known only approximately in a tabular form, we wish to use a Gaussian quadrature formula. Nodes and weights have to be computed using the family of monic orthogonal polynomials, with respect to the weight function e−αx, obtained through the three-term recurrence relation Pk+1(x) = (x + Bk+1)Pk(x) − Ck+1Pk−1(x).

    To guarantee a good precision, we must evaluate carefully the values for the coefficients Bk+1 and Ck+1. Such evaluations are made completely formally through a Mathematica program to obtain great precision.

    A comparison between various methods, starting from moments and modified moments, is shown. Numerical results are also presented.