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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 2(10), Pages 256–268 (Mi msb2126)  

This article is cited in 36 scientific papers (total in 36 papers)

Approximate recovery of periodic functions of several variables

V. N. Temlyakov


Abstract: A linear method is constructed for recovery of functions with bounded mixed difference from values at a fixed number of points. The method gives a recovery error close to the corresponding Kolmogorov width of the class of functions with bounded mixed difference.
Bibliography: 13 titles.

Full text: PDF file (550 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 249–261

Bibliographic databases:

UDC: 517.5
MSC: 41A10, 41A63
Received: 02.02.1984

Citation: V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Mat. Sb. (N.S.), 128(170):2(10) (1985), 256–268; Math. USSR-Sb., 56:1 (1987), 249–261

Citation in format AMSBIB
\Bibitem{Tem85}
\by V.~N.~Temlyakov
\paper Approximate recovery of periodic functions of several variables
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 2(10)
\pages 256--268
\mathnet{http://mi.mathnet.ru/msb2126}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=809488}
\zmath{https://zbmath.org/?q=an:0635.46025}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 249--261
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003034}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Temirgaliev, “Application of the divisors theory to numerical integration of periodic functions in several variables”, Math. USSR-Sb., 69:2 (1991), 527–542  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Din Z., “On the Restoration and One-Sided Limit of Multivariable Periodic-Functions”, 313, no. 4, 1990, 787–790  mathscinet  zmath  isi
    3. Temirgaliev N., “Application of Divisor Theory to Approximate Recovery and Integration of Multivariable Periodical Functions”, 310, no. 5, 1990, 1050–1054  mathscinet  zmath  isi
    4. H Wogniakowski, “Average case complexity of linear multivariate problems II. Applications”, Journal of Complexity, 8:4 (1992), 373  crossref
    5. Wozniakowski H., “Average-Case Complexity of Linear Multivariate Problems”, Bull. Amer. Math. Soc., 29:1 (1993), 70–76  crossref  mathscinet  zmath  isi
    6. Wasilkowski G., Wozniakowski H., “On Strong Tractability of Multivariate Problems”, Information Processing `94, Vol I: Technology and Foundations, Ifip Transactions a-Computer Science and Technology, 51, eds. Pehrson B., Simon I., Elsevier Science Publ B V, 1994, 621–628  crossref  mathscinet  isi
    7. Ritter K. Wasilkowski G.W. Wozniakowski H., “Multivariate Integration and Approximation for Random Fields Satisfying Sacks-Ylvisaker Conditions”, Ann. Appl. Probab., 5:2 (1995), 518–540  crossref  mathscinet  zmath  isi
    8. Wasilkowski G. Wozniakowski H., “Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems”, J. Complex., 11:1 (1995), 1–56  crossref  mathscinet  zmath  isi
    9. Novak E. Ritter K., “High Dimensional Integration of Smooth Functions Over Cubes”, Numer. Math., 75:1 (1996), 79–97  crossref  mathscinet  zmath  isi
    10. Novak E., “On the Power of Adaption”, J. Complex., 12:3 (1996), 199–237  crossref  mathscinet  zmath  isi
    11. Ritter K., Wasilkowski G., “Integration and l-2-Approximation: Average Case Setting with Isotropic Wiener Measure for Smooth Functions”, Rocky Mt. J. Math., 26:4 (1996), 1541–1557  crossref  mathscinet  zmath  isi
    12. Ritter K., Wasilkowski G., “Cubature and Reconstruction of Smooth Isotropic Random Functions”, Z. Angew. Math. Mech., 76:3 (1996), 124–127  mathscinet  zmath  isi
    13. Novak E., Ritter K., “Simple Cubature Formulas with High Polynomial Exactness”, Constr. Approx., 15:4 (1999), 499–522  crossref  mathscinet  zmath  isi
    14. E. D. Nursultanov, N. T. Tleukhanova, “Approximate computation of integrals for functions in $W_p^\alpha[0,1]^n$”, Russian Math. Surveys, 55:6 (2000), 1165–1167  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. E. D. Nursultanov, N. T. Tleukhanova, “Quadrature formulae for classes of functions of low smoothness”, Sb. Math., 194:10 (2003), 1559–1584  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Sh. Azhgaliev, N. Temirgaliev, “Informativeness of Linear Functionals”, Math. Notes, 73:6 (2003), 759–768  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. N. T. Tleukhanova, “Interpolation Formula for Functions of Several Variables”, Math. Notes, 74:1 (2003), 151–153  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. Temlyakov V., “Cubature Formulas, Discrepancy, and Nonlinear Approximation”, J. Complex., 19:3 (2003), 352–391  crossref  mathscinet  zmath  isi
    19. Tleukhanova N., “Interpolation Formula for Multiplicative Transformations of Functions of Several Variables”, Dokl. Math., 67:3 (2003), 340–342  mathscinet  zmath  isi
    20. Fang G., Hickernell F., Li H., “Approximation on Anisotropic Besov Classes with Mixed Norms by Standard Information”, J. Complex., 21:3 (2005), 294–313  crossref  mathscinet  zmath  isi
    21. Kuo F., Sloan I., Wozniakowski H., “Lattice Rules for Multivariate Approximation in the Worst Case Setting”, Monte Carlo and Quasi-Monte Carlo Methods 2004, eds. Niederreiter H., Talay D., Springer-Verlag Berlin, 2006, 289–330  crossref  mathscinet  zmath  isi
    22. Sh. U. Azhgaliev, N. Temirgaliev, “Informativeness of all the linear functionals in the recovery of functions in the classes $H_p^\omega$”, Sb. Math., 198:11 (2007), 1535–1551  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    23. Y.-K. Hu, Y.P. Hu, “Global optimization in clustering using hyperbolic cross points”, Pattern Recognition, 40:6 (2007), 1722  crossref
    24. Gradinaru V., “Fourier Transform on Sparse Grids: Code Design and the Time Dependent Schrodinger Equation”, Computing, 80:1 (2007), 1–22  crossref  mathscinet  zmath  isi
    25. Jiang Yanjie, “Approximation of Anisotropic Classes by Standard Information”, J. Complex., 24:2 (2008), 198–213  crossref  mathscinet  zmath  isi
    26. Gen Sun Fang, Li Qin Duan, “Optimal recovery on the classes of functions with bounded mixed derivative”, Acta Math Sinica, 25:2 (2009), 279  crossref  isi
    27. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. Math., 73:2 (2009), 393–434  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems”, Russian Math. (Iz. VUZ), 54:3 (2010), 45–62  mathnet  crossref  mathscinet  elib
    29. E. S. Smailov, N. T. Tleukhanova, “Estimation of error of cubature formula in Besov space”, Eurasian Math. J., 1:1 (2010), 147–156  mathnet  mathscinet  zmath
    30. Sickel W., Ullrich T., “Spline interpolation on sparse grids”, Appl Anal, 90:3–4 (2011), 337–383  isi
    31. Dinh Dung, “B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness”, J Complexity, 27:6 (2011), 541–567  crossref  isi
    32. Yuan Xiuhua, Ye Peixin, “Monte Carlo Approximation and Integration for Sobolev Classes”, High Performance Networking, Computing, and Communication Systems, Communications in Computer and Information Science, 163, ed. Wu Y., Springer-Verlag Berlin, 2011, 103–110  crossref  isi
    33. Nurlan Nauryzbayev, Nurlan Temirgaliyev, “An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration”, Found Comput Math, 2012  crossref
    34. E. D. Nursultanov, N. T. Tleukhanova, “On reconstruction of multiplicative transformations of functions in anisotropic spaces”, Siberian Math. J., 55:3 (2014), 482–497  mathnet  crossref  mathscinet  isi  elib  elib
    35. Matthew Plumlee, “Fast Prediction of Deterministic Functions Using Sparse Grid Experimental Designs”, Journal of the American Statistical Association, 109:508 (2014), 1581  crossref
    36. V. N. Temlyakov, “Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness”, Sb. Math., 206:11 (2015), 1628–1656  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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