Sulla convergenza di alcune formule di quadratura per il calcolo di integrali a valor principale secondo Cauchy

On the convergence of some quadrature formulas for the computation of Cauchy principal value integrals

Authors

  • Giuliana Criscuolo Instituto per Applicazioni della Matematica, Napoli, Italy
  • Giuseppe Mastroianni Universita di Napoli, Italy
Abstract views: 155

Abstract

Not available.

Downloads

Download data is not yet available.

References

Chawla, M. M.; Ramakrishnan, T. R., Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy type singular integrals. Nordisk Tidskr. Informationsbehandling (BIT) 14 (1974), 14-21, MR0331729, https://doi.org/10.1007/bf01933113

Dzjadik, V. K.(2-AOSUK), Ivanov, V. V.(2-AOSUK-B), On asymptotics and estimates for the uniform norms of the Lagrange interpolation polynomials corresponding to the Chebyshev nodal points. (Russian summary) Anal. Math. 9 (1983), no. 2, 85-97, MR0720078, https://doi.org/10.1007/bf01982005

Elliott, David; Paget, D. F., "On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals" (Numer. Math. 23 (1975), 311-319): an addendum. Numer. Math. 25 (1975/76), no. 3, 287-289, MR0411131, https://doi.org/10.1007/bf01399417

Elliott, David, Paget, D. F., "On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals" (Numer. Math. 23 (1975), 311--319): an addendum. Numer. Math. 25 (1975/76), no. 3, 287-289, MR0411131, https://doi.org/10.1007/bf01399417

Hunter, D. B., Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals. Numer. Math. 19 (1972), 419-424, MR0319355, https://doi.org/10.1007/bf01404924

Ioakimidis, N. I., A direct method for the construction of Gaussian quadrature rules for Cauchy type and finite-part integrals. Anal. Numér. Théor. Approx. 12 (1983), no. 2, 131-140, MR0743131.

Kalandija, A. I., On a direct method of solution of an equation in wing theory with an application to the theory of elasticity. (Russian) Mat. Sb. N.S. 42 (84) 1957 249-272, MR0108079.

Gonska, Heinz H., On approximation by linear operators: improved estimates. Anal. Numér. Théor. Approx. 14 (1985), no. 1, 7-32, MR0830510.

Mastroianni, G., Occorsio, M. R., An algorithm for the numerical evaluation of a Cauchy principal value integral. Ricerche Mat. 33 (1984), no. 1, 3-18, MR0795152.

Mastroianni G., Occorsio M.R., On the numerical evaluation of a Cauchy principal value integral (1984 - to appear).

Monegato, G., The numerical evaluation of one-dimensional Cauchy principal value integrals. Computing 29 (1982), no. 4, 337-354, MR0684742, https://doi.org/10.1007/bf02246760

Piessens, Robert, Numerical evaluation of Cauchy principal values of integrals. Nordisk Tidskr. Informationsbehandling (BIT) 10 1970 476-480, MR0281348, https://doi.org/10.1007/bf01935567

Rabinowitz, Philip, Gaussian integration in the presence of a singularity. SIAM J. Numer. Anal. 4 1967 191-201, MR0213016, https://doi.org/10.1137/0704018

Sikkema, P. C., Der Wert einiger Konstanten in der Theorie der Approximation mit Bernstein-Polynomen. (German) Numer. Math. 3 1961 107-116, MR0123128, https://doi.org/10.1007/bf01386008

Tsamasphyros, G. J.; Theocaris, P. S., On the convergence of a Gauss quadrature rule for evaluation of Cauchy type singular integrals. Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 4, 458-464, MR0468120, https://doi.org/10.1007/bf01933455

Tsamasphyros, G., Theocaris, P. S., On the convergence of some quadrature rules for Cauchy principal-value and finite-part integrals. Computing 31 (1983), no. 2, 105-114, MR0718908, https://doi.org/10.1007/bf02259907

Szegő, Gábor, Orthogonal polynomials. Fourth edition. American Mathematical Society, Colloquium Publications, Vol. XXIII. American Mathematical Society, Providence, R.I., 1975. xiii+432 pp., MR0372517.

Downloads

Published

1985-08-01

How to Cite

Criscuolo, G., & Mastroianni, G. (1985). Sulla convergenza di alcune formule di quadratura per il calcolo di integrali a valor principale secondo Cauchy: On the convergence of some quadrature formulas for the computation of Cauchy principal value integrals. Anal. Numér. Théor. Approx., 14(2), 109–116. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1985-vol14-no2-art2

Issue

Vol. 14 No. 2 (1985)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.