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Generalized Christoffel functions and error of positive quadrature

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Abstract

The author gives some upper and lower bounds for the generalized Christoffel functions related to a Ditzian-Totik generalized weight. As an application, an error estimate of Gauss quadrature formula inL 1-weighted norm is derived.

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References

  1. H. Braß,Quadraturverfahren (Vandenhoeck and Ruprecht, Göttingen, 1977).

    Google Scholar 

  2. G. Criscuolo, G. Mastroianni and G. Monegato, Convergence properties of a class of product formulas for weakly singular integral equations, Math. Comp. 55 (1990) 213–230.

    Google Scholar 

  3. Z. Ditzian and V. Totik,Moduli of Smoothness, S.C.M. (Springer, Berlin, 1987).

    Google Scholar 

  4. R.A. De Vore and R. Scott, Error bounds for Gaussian quadrature and weighted-L1 polynomial approximation, SIAM J. Numer. Anal. 21 (1984) 400–412.

    Google Scholar 

  5. T. Erdélyi, A. Maté and P. Nevai, Inequalities for generalized non-negative polynomials, to appear in Constr. Approx.

  6. T. Erdélyi and P. Nevai, Generalized Jacobi weights, Christoffel functions and zeros of orthogonal polynomials, J. Approx. Theory 69 (1992) 111–132.

    Google Scholar 

  7. G. Freud,Orthogonal Polynomials (Akadémiai Kiadó, Budapest, 1971).

    Google Scholar 

  8. K.J. Förster and K. Petras, On a problem proposed by H. Braß concerning the remainder term in quadrature for convex functions, Numer. Math. 57 (1990) 763–777.

    Google Scholar 

  9. L. Gatteschi, On some orthogonal polynomials integrals, Math. Comp. 35 (1980) 1291–1298.

    Google Scholar 

  10. L. Gatteschi, Uniform approximation of Christoffel numbers for Jacobi weight,Numerical Integration III, Proc. Oberwolfach Conf. 1987, ISNM 85 (1987) pp. 49–59.

    Google Scholar 

  11. W. Gautschi, Computational aspects of orthogonal polynomials, in:Orthogonal Polynomials: Theory and Practice (Kluwer Academic, Nato ASI Series, 1989) pp. 181–216.

  12. G. Mastroianni, Some inequalities including a generalized Ditzian-Totik weight, manuscript.

  13. P. Nevai,Orthogonal Polynomials, Mem. Amer. Math. Soc. 213 (AMS, Providence, RI, 1979).

    Google Scholar 

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

    Google Scholar 

  15. G. Szegö,Orthogonal Polynomials, Amer. Math.SSoc. Colloquium Publications 23 (AMS, Providence, RI, 1975).

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Basilicata, Via N. Sauro 85, I-85100, Potenza, Italy

    G. Mastroianni

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  1. G. Mastroianni
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Dedicated to Prof. Luigi Gatteschi on the occasion of his 70th birthday

Work sponsored by MURST 40%.

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Mastroianni, G. Generalized Christoffel functions and error of positive quadrature. Numer Algor 10, 113–126 (1995). https://doi.org/10.1007/BF02198298

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