Monotony in interpolatory quadratures |
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Authors: | Martin Kütz |
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Institution: | (1) Lehrstuhl E für Mathematik, Technische Universität Braunschweig, Pockelsstr. 14, D-3300 Braunschweig, FRG |
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Abstract: | Summary Let
, be holomorphic in an open disc with the centrez
0=0 and radiusr>1. LetQ
n
(n=1, 2, ...) be interpolatory quadrature formulas approximating the integral
. In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ
n
9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule. |
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Keywords: | AMS(MOS): 65D30 CR: 5 16 |
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