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Product type quadrature formulas

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Abstract

This paper is concerned with the numerical approximation of integrals of the formε b a f(x)g(x)dx by means of a product type quadrature formula. In such a formula the functionf (x) is sampled at a set ofn+1 distinct points and the functiong(x) at a (possibly different) set ofm+1 distinct points. These formulas are a generalization of the classical (regular) numerical integration rules. A number of basic results for such formulas are stated and proved. The concept of a symmetric quadrature formula is defined and the connection between such rules and regular quadrature formulas is discussed. Expressions for the error term are developed. These are applied to a specific example.

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Author notes

  1. W. Robert Boland

    Present address: Department of Mathematics, Clemson University, 29631, Clemson, S.C.

Authors and Affiliations

  1. Department of Mathematics, Drexel University, 19104, Philadelphia, Pennsylvania, USA

    W. Robert Boland & C. S. Duris

Authors
  1. W. Robert Boland
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  2. C. S. Duris
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Additional information

The work of the first author was supported in part by NIH Grant No. FRO 7129-01 and that of the second author in part by U.S. Army Ballistic Research Laboratories Contract DA-18-001-AMC-876 X.

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Boland, W.R., Duris, C.S. Product type quadrature formulas. BIT 11, 139–158 (1971). https://doi.org/10.1007/BF01934362

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  • DOI: https://doi.org/10.1007/BF01934362

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