Skip to main content
SpringerLink
Log in

Sulla convergenza delle formule di quadratura del tipo Gauss-Lobatto per il calcolo di integrali singolari V.P.

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

The author considers Gauss-Lobatto rules for evaluating of Cauchy singular integrals with respect to a generalized smooth Jacobi weight.

Convergence theorems are given, and some estimates of the remainder are established. The previous results are generalized and improved.

Sommario

L’autore considera formule di quadratura del tipo Gauss-Lobatto per il calcolo di integrali a valor principale secondo Cauchy rispetto ad un peso generalizzato regolare di Jacobi.

Vengono dimostrati teoremi di convergenza e stabilite alcune stime dell’errore. Si generalizzano e migliorano, inoltre, precedenti risultati.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliografia

  1. G. Criscuolo, G. Mastroianni,Formule Gaussiane per il calcolo di integrali a valor principale secondo Cauchy e loro convergenza, Calcolo, XXII, (1985) 391–411.

    MathSciNet  Google Scholar 

  2. G. Criscuolo, G. Mastroianni,Sulla convergenza di alcune formule di quadratura per il calcolo di integrali a valor principale secondo Cauchy, Anal. Numér. Théor. Approx., 14, (1985) 109–116.

    MATH  MathSciNet  Google Scholar 

  3. G. Criscuolo, G. Mastroianni,On the convergence of the Gauss quadrature rules for Cauchy principal value integrals, Ricerche Mat., XXXV, (1986) 45–60.

    MathSciNet  Google Scholar 

  4. G. Criscuolo, G. Mastroianni,On the convergence of Gauss-Christoffel formula with preassigned node for Cauchy principal value integrals, J. Approx. Theory, 49, (1987).

  5. H. Esser,Konvergenz von quadraturverfahren vom Gausschen typ. Studia Scientarum Mathematicarum Hungarica, 7, (1972) 375–378.

    MathSciNet  Google Scholar 

  6. D.S. Lubinsky, P. Rabinowitz,Rates of convergence of Gaussian quadrature for singular integrands, Math. Comp. 43 (167), (1984) 219–242.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Rabinowitz,On the convergence of Hunter’s method for Cauchy principal value integrals. In Numerical Solution of Singular Integral Equations, 1984. Edited by A. Gerasoulis and R. Vichnevetsky IMACS.

  8. P. Nevai,Mean convergence of Lagrange interpolation III. Trans. Amer. Math. Soc. 2 (282), 1984, 669–698.

    Article  MathSciNet  Google Scholar 

  9. P. O. Runck,Bemerkungen zu den Approximationssätzen von Jackson und Jackson-Timan. In «ISNM 10, Abstract Spaces and Approximation, Proc. of conf. Oberwolfach, 1968» (P. L. Butzer and Sz. Nagy, eds) 303–308, Birkäuser, Basel, 1969.

    Google Scholar 

  10. C. A. Micchelli, A. Sharma,On a problem of Turan: multiple node Gaussian quadrature,Rend. Mat. (VIII) 3 (3), (1983) 529–551.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto per Applicazioni della Matematica, C.N.R., V.le A. Gramsci 5, 80122, Napoli

    G. Criscuolo

Authors
  1. G. Criscuolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Criscuolo, G. Sulla convergenza delle formule di quadratura del tipo Gauss-Lobatto per il calcolo di integrali singolari V.P.. Calcolo 23, 161–174 (1986). https://doi.org/10.1007/BF02579427

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579427

Subject Classification

Key words

Search

Navigation