Approximative capabilities of “Smolyak type-computational aggregates with Dirichlet, Fejér and Valleé-Poussin kernels in the scale of Ul’yanov classes

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• 作者：N. Temirgaliev ; N. Zh. Nauryzbayev ; A. A. Shomanova
• 关键词：recovering operator ; error of the recovery ; tensor product of functionals ; Feje′ r kernel ; Dirichlet kernel ; Valle′ e ; Poussin kernel ; Korobov classes ; Ul’yanov classes.
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：59
• 期：7
• 页码：67-72
• 全文大小：476 KB
• 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.