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The convergence of interpolatory product integration rules

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Abstract

Conditions are given for the convergence of product integration rules based on the zeros of orthogonal polynomials associated with a generalized smooth Jacobi weight, possibly augmented by one or both endpoints.

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References

  1. P. J. Davis and P. Rabinowitz,Methods of Numerical Integration, Second Edition, Academic Press, New York, 1984.

    Google Scholar 

  2. D. Elliott and D. F. Paget,Product-integration rules and their convergence, BIT 16 (1976) 32–40.

    Google Scholar 

  3. D. Elliott and D. F. Paget,The convergence of product integration rules, BIT 18 (1978) 137–141.

    Article  Google Scholar 

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

    Google Scholar 

  5. I. H. Sloan,On the numerical evaluation of singular integrals, BIT 18 (1978) 91–102.

    Google Scholar 

  6. I. H. Sloan and W. E. Smith,Product-integration with the Clenshaw-Curtis and related points. Convergence properties, Numer. Math. 30 (1978) 415–428.

    Article  Google Scholar 

  7. I. H. Sloan and W. E. Smith,Properties of interpolatory product integration rules, SIAM J. Numer. Anal. 19 (1982) 427–442.

    Article  Google Scholar 

  8. W. E. Smith and I. H. Sloan,Product-integration rules based on the zeros of Jacobi polynomials, SIAM J. Numer. Anal. 17 (1980) 1–13.

    Article  Google Scholar 

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Rabinowitz, P. The convergence of interpolatory product integration rules. BIT 26, 131–134 (1986). https://doi.org/10.1007/BF01939370

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  • DOI: https://doi.org/10.1007/BF01939370

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