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Asymptotic properties of minimum norm and optimal quadratures

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Summary

This paper contains three types of asymptotic results for certain quadratures applied to a Hilbert space of analytic functions. These results concern the following: bounds on the norm of a certain error functional; the convergence of the weights and nodes of a minimum norm quadrature to the weights and nodes of the corresponding Gaussian quadrature; and the convergence of optimal quadratures.

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Authors and Affiliations

  1. Department of Mathematics, University of Utah, 206 Mathematics Building, 84112, Salt Lake City, Utah, USA

    Robert E. Barnhill

  2. Department of Mathematics, University of Utah, Salt Lake City, Utah

    Robert E. Barnhill

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  1. Robert E. Barnhill
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Additional information

The research reported in this document was supported by the Office of Naval Research, Contract Nonr 562(36) to Brown University and by the National Science Foundation, Grant GP 5906 to the University of Utah.

On leave during the 1966–67 academic year at the Division of Applied Mathematics, Brown University, Providence, Rhode Island.

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Barnhill, R.E. Asymptotic properties of minimum norm and optimal quadratures. Numer. Math. 12, 384–393 (1968). https://doi.org/10.1007/BF02161361

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  • DOI: https://doi.org/10.1007/BF02161361

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