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Product Inequalities and Weighted Quadrature

In: Ostrowski Type Inequalities and Applications in Numerical Integration

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  • John Roumeliotis

    (Victoria University, School of Communications and Informatics)

Abstract

Weighted (or product) integral inequalities are developed via Ostrowski and Griiss approaches. The inequalities provide an error estimate for weighted integrals where both the quadrature rule and error bound are given in terms of (at most) the first three moments of the weight. Rule type is distinguished and interior point, boundary point and three point rules are explored. Results for the most popular weight functions are tabulated. Numerical experiments are provided and comparisons with other product rules of similar order are made. The methods outlined in this chapter allow for the generation of non-uniform quadrature grids with respect to any arbitrary weight employing only a small number of weight moments.

Suggested Citation

  • John Roumeliotis, 2002. "Product Inequalities and Weighted Quadrature," Springer Books, in: Sever S. Dragomir & Themistocles M. Rassias (ed.), Ostrowski Type Inequalities and Applications in Numerical Integration, chapter 0, pages 373-416, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2519-4_7
    DOI: 10.1007/978-94-017-2519-4_7
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