Zur Existenz optimaler Quadraturformeln mit freien Knoten bei Integration analytischer Funktionen |
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| Authors: | Dr. Augustin Paulik |
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| Affiliation: | (1) Lehrstühle für Numerische und Angewandte Mathematik der Universität Göttingen, Lotzestr. 16-18, D-3400 Göttingen, Bundesrepublik Deutschland |
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| Abstract: | Summary In the present paper we discuss the optimal quadrature rules for integration with positive continuous weight function in Hardy space H2 of functions analytic in a circle of the complex plane. The new representations of the optimal weights and the norm of the error functional as functions of the nodes are obtained. On this basis we give an elementary proof for the existence of the optimal quadrature formula with free nodes. |
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