Displaying similar documents to “Polynomial approximation and the quadrature problem over a semi-infinite interval”

Numerical integration with highly oscillating weight functions

Jozef Mikloško (1970)

Aplikace matematiky

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The paper describes a new numerical method for the computation of integrals with the weight function exp ( i k x ) , k integer, which can be used for improper and multiple integrals. The compound rules of this method use parameters, of weighted quadratures of Gauss type which are tabulated for various k . The using of the method especially for high k is demonstrated by numerical experiments.

Further convergence results for two quadrature rules for Cauchy type principal value integrals

Nikolaos I. Ioakimidis (1982)

Aplikace matematiky

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New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to 1 2 . The results obtained...