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Gaussian,Lobatto and Radau positive quadrature rules with a prescribed abscissa |
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| Authors: | Bernhard Beckermann Jorge Bustamante Reinaldo Martínez-Cruz José M. Quesada |
| Affiliation: | 1. Laboratoire Painlevé UMR 8524 (ANO-EDP), UFR Mathématiques, M3, UST Lille, 59655, Villeneuve d’Ascq Cedex, France 2. Facultad de Ciencias Físico-Matemáticas (FCFM), Benemerita Universidad Autonoma de Puebla (BUAP), Apartado Postal 1152, Pue. C.P. 72000, Puebla, México 3. Departamento de Matemáticas, Universidad de Jaén, Jaén, Spain |
| Abstract: | For a given $theta in (a,b)$ , we investigate the question whether there exists a positive quadrature formula with maximal degree of precision which has the prescribed abscissa $theta $ plus possibly $a$ and/or $b$ , the endpoints of the interval of integration. This study relies on recent results on the location of roots of quasi-orthogonal polynomials. The above positive quadrature formulae are useful in studying problems in one-sided polynomial $L_1$ approximation. |
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