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Gauss-turán quadratures of chebyshev type and error formulae

Gauß-Turán-Quadratur des Chebyshev-Typs und ihre Restformeln

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Abstract

This paper begins with an investigation of two special forms of the Gauss-Turán quadrature of Chebyshev-type of precision 6n−1. Then the remainder formulas of these quadratures are developed and sharp error bounds for the functions inC q[−1, 1] are shown, whereq is a positive integer. Most importantly this study proves that these reslts can be extended in order to yield sharp error estimates for all such quadratures of higher precision.

Zusammenfassung

Dieser Aufsatz fängt mit einer Untersuchung zweier besonderer Gestalten der Gauß-Turán-Quadratur des Chebyshev-Typs der Präzision 6n−1 an. Dann werden die Restformeln dieser Quadraturen entwickelt und scharfe Irrtumgrenzen für die Funktionen inC q[−1, 1] gezeigt, woq eine positive ganze Zahl ist. Am wichtigsten beweist diese Studie, daß diese Ergebnisse verlängert werden können, um die Resformeln und scharfe Irrtumsabschätzungen für alle solchen Quadraturen höherer Präzision zu erhalten.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA, U.S.A.

    R. D. Riess

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  1. R. D. Riess
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Riess, R.D. Gauss-turán quadratures of chebyshev type and error formulae. Computing 15, 173–179 (1975). https://doi.org/10.1007/BF02242365

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