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Gaussian rational quadrature formulas for ill-scaled integrands

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J. R. Illán GonzálezAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 233, Issue 3

Pages 745 - 748

https://doi.org/10.1016/j.cam.2009.02.043

Published: 01 December 2009 Publication History

Abstract

A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral @!"If(x)W(x)dx, when f is meromorphic in a neighborhood V of the interval I and W(x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi's method.

References

[1]

Gautschi, W., Algorithm 793: GQRAT-Gauss quadrature for rational functions. ACM Trans. Math. Software. v25. 213-239.

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[2]

Gautschi, W., Orthogonal polynomials. Computation and approximation. In: Numerical Mathematics and Scientific Computation, Oxford University Press, New York.

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[3]

Fidalgo Prieto, U., Illán González, J.R. and López Lagomasino, G., Convergence and computation of simultaneous rational quadrature formulas. Numer. Math. v106. 99-128.

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[4]

Illán González, J.R. and López-Lagomasino, G., A numerical approach for Gaussian rational formulas to handle difficult poles. In: Topping, Montero, (Eds.), Proceedings of the Fifth Internat. Conf. on Engineering Computational Technology, Civil-Comp Press, Stirlingshire, UK.

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Illn-Gonzlez JRebollido-Lorenzo J(2017)Evaluation of finite part integrals using a regularization technique that decreases instabilityJournal of Computational and Applied Mathematics10.1016/j.cam.2017.01.009319:C(210-219)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1016/j.cam.2017.01.009
(2015)Gauss rules associated with nearly singular weightsApplied Numerical Mathematics10.1016/j.apnum.2014.07.00691:C(1-10)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1016/j.apnum.2014.07.006

Gaussian rational quadrature formulas for ill-scaled integrands
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
    2. Numerical analysis
2. Theory of computation

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 233, Issue 3

December, 2009

268 pages

ISSN:0377-0427

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 December 2009

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Illn-Gonzlez JRebollido-Lorenzo J(2017)Evaluation of finite part integrals using a regularization technique that decreases instabilityJournal of Computational and Applied Mathematics10.1016/j.cam.2017.01.009319:C(210-219)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1016/j.cam.2017.01.009
(2015)Gauss rules associated with nearly singular weightsApplied Numerical Mathematics10.1016/j.apnum.2014.07.00691:C(1-10)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1016/j.apnum.2014.07.006

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Scaled asymptotics for some q-functions

Convergence and computation of simultaneous rational quadrature formulas

Quadratures associated with pseudo-orthogonal rational functions on the real half line with poles in [-∞, 0]

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