Displaying similar documents to “New results in extremal problems with polynomials.”

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...

Generalized Kronrod Patterson type imbedded quadratures

Sylvan Elhay, Jaroslav Kautský (1992)

Applications of Mathematics

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We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.