On Double Chebyshev Series Approximation

Abstract

Previous article Next article On Double Chebyshev Series ApproximationN. K. BasuN. K. Basuhttps://doi.org/10.1137/0710045PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractMany of the standard practical techniques for Chebyshev polynomial approximation in one-variable problems have been extended to two-variable problems.[1] Ferdinand Freudenstein, Bi-variate, rectangular, optimum-interval interpolation, Math. Comp., 15 (1961), 288–291 MR0129532 0168.14903 CrossrefGoogle Scholar[2] C. W. Clenshaw, A note on the summation of Chebyshev series, Math. Tables Aids Comput., 9 (1955), 118–120 MR0071856 0065.05403 CrossrefGoogle Scholar[3] David Elliott, Error analysis of an algorithm for summing certain finite series, J. Austral. Math. Soc., 8 (1968), 213–221 MR0230452 0159.45104 CrossrefGoogle Scholar[4] David Elliott, The numerical solution of integral equations using Chebyshev polynomials, J. Austral. Math. Soc., 1 (1959/1960), 344–356 MR0128087 0096.10201 CrossrefGoogle Scholar[5] L. Fox and , E. T. Goodwin, The numerical solution of non-singular linear integral equations, Philos. Trans. Roy. Soc. London. Ser. A., 245 (1953), 501–534 MR0054355 0050.12902 CrossrefISIGoogle Scholar[6] Google Scholar[7] L. Fox and , I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London, 1968ix+205 MR0228149 0153.17502 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Analytical and numerical investigation of Poiseuille flow through semi-elliptic annulusPhysics of Fluids, Vol. 34, No. 8 | 1 Aug 2022 Cross Ref Study of the free surface Green function at zero forward speed in finite water depth using Newman’s methodApplied Ocean Research, Vol. 120 | 1 Mar 2022 Cross Ref Comparison of existing methods for the calculation of the infinite water depth free-surface Green function for the wave–structure interaction problemApplied Ocean Research, Vol. 81 | 1 Dec 2018 Cross Ref Nondimensionalized Univariate Equation Characterizing Optimal State Feedback Control for Collision AvoidanceIEEE Transactions on Intelligent Transportation Systems, Vol. 19, No. 10 | 1 Oct 2018 Cross Ref The automatic solution of partial differential equations using a global spectral methodJournal of Computational Physics, Vol. 299 | 1 Oct 2015 Cross Ref Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flowJournal of Differential Equations, Vol. 257, No. 8 | 1 Oct 2014 Cross Ref A new kind of double Chebyshev polynomial approximation on unbounded domainsBoundary Value Problems, Vol. 2013, No. 1 | 22 January 2013 Cross Ref On Approximate Solutions of Second-Order Linear Partial Differential EquationsApplied Mathematics, Vol. 03, No. 09 | 1 Jan 2012 Cross Ref A fitting formula for the falloff curves of unimolecular reactions, II: Tunneling effectsInternational Journal of Chemical Kinetics, Vol. 43, No. 1 | 19 October 2010 Cross Ref Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic fieldInternational Journal for Numerical Methods in Fluids, Vol. 419 | 1 Jan 2009 Cross Ref Large and small signal distortion analysis using modified Volterra seriesAnalog Integrated Circuits and Signal Processing, Vol. 54, No. 2 | 29 November 2007 Cross Ref Volterra Analysis Using Chebyshev Series2007 IEEE International Symposium on Circuits and Systems | 1 May 2007 Cross Ref Large and Small Signal Distortion Analysis Using Modified Volterra Series2006 NORCHIP | 1 Nov 2006 Cross Ref An efficient numerical approximation for the linear class of mixed integral equationsApplied Mathematics and Computation, Vol. 167, No. 2 | 1 Aug 2005 Cross Ref Chebyshev polynomial solutions of second-order linear partial differential equationsApplied Mathematics and Computation, Vol. 134, No. 1 | 1 Jan 2003 Cross Ref Chebyshev series solution of linear Fredholm integrodifferential equationsInternational Journal of Mathematical Education in Science and Technology, Vol. 29, No. 4 | 1 Jul 1998 Cross Ref Fast polynomial multiplication and convolutions related to the discrete cosine transformLinear Algebra and its Applications, Vol. 252, No. 1-3 | 1 Feb 1997 Cross Ref Chebyshev series solutions of Fredholm integral equationsInternational Journal of Mathematical Education in Science and Technology, Vol. 27, No. 5 | 9 July 2006 Cross Ref An algorithm for the evaluation of multidimensional (direct and inverse) discrete Chebyshev transformsJournal of Computational and Applied Mathematics, Vol. 8, No. 4 | 1 Dec 1982 Cross Ref Optimum acoustic design of free-running low speed propellersAircraft Systems and Technology Meeting | 16 August 1977 Cross Ref Clenshaw sums in several variablesConstructive Theory of Functions of Several Variables | 2 October 2006 Cross Ref Volume 10, Issue 3| 1973SIAM Journal on Numerical Analysis History Submitted:05 March 1971Published online:14 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0710045Article page range:pp. 496-505ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics