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2006 | 4 | 3 | 435-448
Tytuł artykułu

Accelerating the convergence of trigonometric series

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
3
Strony
435-448
Opis fizyczny
Daty
wydano
2006-09-01
online
2006-09-01
Twórcy
Bibliografia
  • [1] G.A. Baker and P. Graves-Morris: Pade Approximants. Encyclopedia of mathematics and its applications, 2nd ed., Cambridge Univ. Press, Cambridge, 1996.
  • [2] G. Baszenski, F.-J. Delvos and M. Tasche: “A united approach to accelerating trigonometric expansions”, Comput. Math. Appl., Vol. 30(3–6), (1995), pp. 33–49. http://dx.doi.org/10.1016/0898-1221(95)00084-4
  • [3] W. Cai, D. Gottlieb and C.W. Shu: “Essentially non oscillatory spectral Fourier methods for shock wave calculations”, Math. Comp., Vol. 52, (1989), pp. 389–410. http://dx.doi.org/10.2307/2008473
  • [4] E.W. Cheney: Introduction to Approximation Theory, McGraw-Hill, New York, 1996.
  • [5] K.S. Eckhoff: “Accurate and efficient reconstruction of discontinuous functions from truncated series expansions”, Math. Comp., Vol. 61, (1993), pp. 745–763. http://dx.doi.org/10.2307/2153251
  • [6] K.S. Eckhoff: “Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions”, Math. Comp., Vol. 64, (1995), pp. 671–690. http://dx.doi.org/10.2307/2153445
  • [7] K.S. Eckhoff: “On a high order numerical method for functions with singularities”, Math. Comp., Vol. 67, (1998), pp. 1063–1087. http://dx.doi.org/10.1090/S0025-5718-98-00949-1
  • [8] C.E. Wasberg: On the numerical approximation of derivatives by a modified Fourier collocation method, Thesis (PhD), Department of Mathematics, University of Bergen, Norway, 1996.
  • [9] T.A. Driscoll and B. Fornberg: “A Pade-based algorithm for overcoming the Gibbs phenomenon”, Numerical Algorithms, Vol. 26, (2000), pp. 77–92. http://dx.doi.org/10.1023/A:1016648530648
  • [10] J. Geer: “Rational trigonometric approximations using Fourier series partial sums”, J. Sci. Computing, Vol. 10(3), (1995), pp. 325–356. http://dx.doi.org/10.1007/BF02091779
  • [11] D. Gottlieb: “Spectral methods for compressible flow problems”, In: Soubbaramayer and J.P. Boujot (Eds.): Proc. 9th Internat. Conf. Numer. Methods Fluid Dynamics, Lecture Notes in Phys., Vol. 218, Saclay, France, Springer-Verlag, Berlin and New York, 1985, pp. 48–61.
  • [12] D. Gottlieb: “Issues in the application of high order schemes”, In: M.Y. Hussaini, A. Kumar and M.D. Salas (Eds): Proc. Workshop on Algorithmic Trends in Computational Fluid Dynamics (Hampton, Virginia, USA), Springer-Verlag, ICASE /NASA LaRC Series, 1991, pp. 195–218.
  • [13] D. Gottlieb, L. Lustman and S.A. Orszag: “Spectral calculations of one-dimensional inviscid compressible flows”, SIAM J. Sci. Statist. Comput., Vol. 2, (1981), pp. 296–310. http://dx.doi.org/10.1137/0902024
  • [14] D. Gottlieb, C.W. Shu, A. Solomonoff and H. Vandevon: “On the Gibbs Phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function”, J. Comput. Appl. Math., Vol. 43, (1992), pp. 81–92. http://dx.doi.org/10.1016/0377-0427(92)90260-5
  • [15] D. Gottlieb and C.W. Shu: On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a sub-interval from the spectral partial sum of a piecewise analytic function, ICASE report, 1993, pp. 93–82.
  • [16] D. Gottlieb and C.W. Shu: “On the Gibbs phenomena IV: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function”, Math. Comp., Vol. 64, (1995), pp. 1081–1096. http://dx.doi.org/10.2307/2153484
  • [17] D. Gottlieb and C.W. Shu: “On the Gibbs Phenomenon V: Recovering Exponential Accuracy from collocation point values of a piecewise analytic function”, Numer. Math., Vol. 33, (1996), pp. 280–290.
  • [18] W.B. Jones and G. Hardy: “Accelerating Convergence of Trigonometric Approximations”, Math. Comp., Vol. 24, (1970), pp. 47–60. http://dx.doi.org/10.2307/2004830
  • [19] A. Krylov: On an approximate calculations, Lectures delivered in 1906 (in Russian), St Peterburg, Tipolitography of Birkenfeld, 1907.
  • [20] C. Lanczos: “Evaluation of noisy data”, J. Soc. Indust. Appl. Math., Ser. B Numer. Anal., Vol. 1, (1964), pp. 76–85.
  • [21] C. Lanczos: Discourse on Fourier Series, Oliver and Boyd, Edinburgh, 1966.
  • [22] P.D. Lax: “Accuracy and resolution in the computation of solutions of linear and nonlinear equations”, In: C. de Boor and G.H. Golub (Eds.): Recent Advances in Numerical Analysis, Proc. Symposium Univ of Wisconsin-Madison, Academic Press, New York, 1978, pp. 107–117.
  • [23] J.N. Lyness: “Computational Techniques Based on the Lanczos Representation”, Math. Comp., Vol. 28, (1974), pp. 81–123. http://dx.doi.org/10.2307/2005818
  • [24] A. Nersessian: “Bernoulli type quasipolynomials and accelerating convergence of Fourier Series of piecewise smooth functions (in Russian)”, Reports of NAS RA, Vol. 104(4), (2004), pp. 186–191.
  • [25] A. Nersessian and A. Poghosyan: “Bernoulli method in multidimensional case”, Preprint No20 Ar-00, Deposited in ArmNIINTI 09.03.00, (2000), pp. 1–40 (in Russian).
  • [26] A. Nersessian and A. Poghosyan: “On a rational linear approximation on a finite interval”, Reports of NAS RA, Vol. 104(3), (2004), pp. 177–184 (in Russian).
  • [27] A. Nersessian and A. Poghosyan: “Asymptotic estimates for a nonlinear acceleration method of Fourier series”, Reports of NAS RA (in Russian), to be published.
  • [28] A. Nersessian and A. Poghosyan: “Asymptotic errors of accelerated two-dimensional trigonometric approximations”, In: G.A. Barsegian, H.G.W. Begehr, H.G. Ghazaryan and A. Nersessian (Eds.): Complex Analysis, Differential Equations and Related Topics, Yerevan, Armenia, September 17–21, 2002, “Gitutjun” Publishing House, Yerevan, Armenia, 2004, pp. 70–78.
  • [29] A. Poghosyan: “On a convergence of a rational trigonometric approximation”, In: G.A. Barsegian, H.G.W. Begehr, H.G. Ghazaryan and A. Nersessian (Eds.): Complex Analysis, Differential Equations and Related Topics, Yerevan, Armenia, September 17–21, 2002, “Gitutjun” Publishing House, Yerevan, Armenia, 2004, pp. 79–87.
  • [30] A. Nersessian and A. Poghosyan: “On a rational linear approximation Fourier Series for smooth functions”, J. Sci. Comput., to be published.
  • [31] S. Wolfram: The MATHEMATICA book, 4th ed., Wolfram Media, Cambridge University Press, 1999.
  • [32] A. Zygmund: Trigonometric Series, Vol. 1,2, Cambridge Univ. Press, Cambridge, 1959.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0016-7
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