参考文献:1.Smolyak, S. A. “Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,-Dokl. Akad. Nauk SSSR textbf148, No. 4, 240-43 (1963). 2.Smolyak, S. A. “Optimal Recovery of Functions and Functionals of Functions,-Candidate’s Dissertation in Mathematics and Physics (Moscow, 1965). 3.Temirgaliev, N. “Classes of Us (β, θ,α; ψ) andQuadrature Formulas,-Dokl.AkadNauk 393,No. 5, 605-08 (2003).MathSciNet 4.Temirgaliev, N. “Tensor Products of Functionals and their Application,-Dokl. Math. 81, No. 1, 78-2 (2010).MATH MathSciNet View Article 5.Korobov, N.M. Theoretical Numerical Methods in Approximate Analysis (Fizmatgiz, Moscow, 1963) [in Russian]. 6.Temirgaliev, N., Kudaibergenov, S. S., Shomanova, A. A. “Applications of Smolyak Quadrature Formulas to theNumerical Integration of FourierCoefficients and in Function Recovery Problems,”RussianMathematics (Iz. VUZ) 54, No. 3, 45-2 (2010).MATH MathSciNet 7.Nauryzbayev, N., Temirgaliyev, N. “An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration,-Found. Comput.Math. 12, No. 2, 139-72 (2012).MATH MathSciNet View Article 8.Temirgaliev, N., Kudaibergenov, S. S., Shomanova, A. A. “An Application of Tensor Products of Functionals in Problems of Numerical Integration,-Izv. Math. 73, No. 2, 393-34 (2009).MATH MathSciNet View Article 9.Paskov, S. “Average Case Complexity for Multivariate Integration for Smooth Functions,-J. Complexity 9, No. 2, 291-12 (1993).MATH MathSciNet View Article 10.Wasilkowski, G., Woz′ niakowski, H. “Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems,-J. Complexity 11, No. 1, 1-6 (1995).MATH MathSciNet View Article
作者单位:N. Temirgaliev (1) N. Zh. Nauryzbayev (1) A. A. Shomanova (1)
1. L. N. Gumilev Eurasian National University, ul. Mirzoyana 2, Astana, 010008, Republic of Kazakhstan
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Mathematics Russian Library of Science
出版者:Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
ISSN:1934-810X
文摘
In Ul’yanov classes, we compare computational aggregates constructed by the method of tensor products of functionals by means of trigonometric Fourier series.