We study the behavior of some “truncated” Gaussian rules based on the zeros of Pollaczek-type polynomials. These formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces. Moreover, we apply these results to the related Lagrange interpolation process and to prove the stability and the convergence of a Nyström method for Fredholm integral equations of the second kind. Finally, some numerical examples are shown.
Gaussian quadrature rules with exponential weights on (-1,1)
DE BONIS, Maria Carmela;MASTROIANNI, Giuseppe Maria;NOTARANGELO, INCORONATA
2012-01-01
Abstract
We study the behavior of some “truncated” Gaussian rules based on the zeros of Pollaczek-type polynomials. These formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces. Moreover, we apply these results to the related Lagrange interpolation process and to prove the stability and the convergence of a Nyström method for Fredholm integral equations of the second kind. Finally, some numerical examples are shown.File in questo prodotto:
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