Error estimates for some quadrature rules with maximal trigonometric degree of exactness (Q2875741)
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scientific article; zbMATH DE number 6328589
| Language | Label | Description | Also known as |
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| English | Error estimates for some quadrature rules with maximal trigonometric degree of exactness |
scientific article; zbMATH DE number 6328589 |
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Error estimates for some quadrature rules with maximal trigonometric degree of exactness (English)
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11 August 2014
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trigonometric polynomial
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trigonometric degree of exactness
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Gaussian quadrature
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error estimate
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Several error estimates are given for quadrature formulas on \([-\pi, \pi]\) with maximal trigonometric degree of exactness, where the weight functions are even on \((-\pi, \pi)\) and the quadratures are applied to functions satisfying certain analytic properties. \vskip .1 in The main tools for the paper involve relationships between Gaussian quadrature formulas of modified weight functions (for example, \(w(x)\) and \(w(x) \sqrt{\frac{1-x}{1+x}}\)) and a theorem on the error in cubature formulae for analytic functions by \textit{W. Gautschi} and \textit{R. S. Varga} [SIAM J. Numer. Anal. 20, 1170--1186 (1983; Zbl 0545.41040)].
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