Gaussian Quadrature Rules with Simple Node-Weight Relations |
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Authors: | EXL de Andrade CF Bracciali A Sri Ranga |
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Institution: | (1) Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto, SP, Brazil |
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Abstract: | In this paper, we consider the symmetric Gaussian and L-Gaussian quadrature rules associated with twin periodic recurrence relations with possible variations in the initial coefficient. We show that the weights of the associated Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 4. We also show that the weights of the associated L-Gaussian quadrature rules can be given as rational functions in terms of the corresponding nodes where the numerators and denominators are polynomials of degree at most 5. Special cases of these quadrature rules are given. Finally, an easy to implement procedure for the evaluation of the nodes is described. |
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Keywords: | orthogonal polynomials Gaussian quadrature rules L-Gaussian quadrature rules |
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