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J. Girshovich, Extremal properties of Euler-Maclaurin
and Gregory quadrature formulas, Eesti Nsv Teaduste Akadeemia Toimetised. Füüsika. Matemaatika, 27 (1978) no. 3, p. 259-265. It is known that the modified Euler-Maclaurin quadrature formula is the best quadrature formula in the sense of A. Sard of certain form for set . We show that this formula is still optimal if variable nodes are allowed, and trapezoidal rule is the optimal formula for certain subset of . As a result, we obtain that the Gregory quadrature formula is asymptotically optimal for the set . |
gum1978.pdf | 241309 |
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A. N. Ignatyev, About calculation of norm of the error functional
of a quadrature formula with a boundary layer in Lebesgue spaces, The manuscript is a deposit in VINITI on July 28, 1999 no. 2475-B99, Ufa: Institute of mathematics with computer center UfSC RAS, 1999, 24 p. In the manuscript "the class of quadrature formulas with a boundary layer as expansion of a class of composite quadrature formulas is defined. The way of calculation of norms of error functional of quadrature formulas with a boundary layer in Lebesgue spaces is specified". |
ian1999.pdf | 288919 |
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A. N. Ignatyev, About the derivative of a boundary layer function, Optimization of numerical methods: Proceedings of the International scientific conference "Optimization of numerical methods", dedicated to 90 years from birthday of Sergey L'vovitsch Sobolev (1908-1989). Part I, Ufa: Institute of mathematics with computer center UfSC RAS, 2000, 97-103 p. The mutually unequivocal conformity between the quadrature formulas with simple weight function and interpolating formulas of a special kind is established, if the left boundary layer of quadrature formula supplements right boundary layer up to unit. This conformity allows to prove properties of the quadrature formulas through the reference to properties of the interpolating formulas. |
ian2000.pdf | 1837639 |