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A Survey of Methods for Rational Approximation, with Particular Reference to a New Method Based on a Forumla of Darboux

1963; Society for Industrial and Applied Mathematics; Volume: 5; Issue: 3 Linguagem: Inglês

10.1137/1005065

1095-7200

E. W. Cheney, Thomas H. Southard,

Numerical Methods and Algorithms

Previous article Next article A Survey of Methods for Rational Approximation, with Particular Reference to a New Method Based on a Forumla of DarbouxE. W. Cheney and T. H. SouthardE. W. Cheney and T. H. Southardhttps://doi.org/10.1137/1005065PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307 MR0095369 0072.28403 Google Scholar[2] D. Jackson, The Theory of Approximation, Vol. XI, Amer. Math. Soc. Colloquium Publications, New York, 1930 Google Scholar[3] G. Darboux, Sur les Développements en Série des Functions d'une Seule Variable, J. Math. Purer Appl., 41 (1876), 291–312 Google Scholar[4] E. T. Whittaker and , G. N. Watson, A Course of Modern Analysis, Cambridge, 1950 Google Scholar[5] P. M. Hummel and , C. L. Seebeck, Jr., A generalization of Taylor's expansion, Amer. Math. 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Phys., 34 (1955), 1–42 MR0068901 0067.28602 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Adaptive sampling applied to multivariate, multiple output rational interpolation models with application to microwave circuitsInternational Journal of RF and Microwave Computer-Aided Engineering, Vol. 12, No. 4 | 19 June 2002 Cross Ref Creating accurate multivariate rational interpolation models of microwave circuits by using efficient adaptive sampling to minimize the number of computational electromagnetic analysesIEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 8 | 1 Aug 2001 Cross Ref Approximation in normed linear spacesNumerical Analysis: Historical Developments in the 20th Century | 1 Jan 2001 Cross Ref Approximation in normed linear spacesJournal of Computational and Applied Mathematics, Vol. 121, No. 1-2 | 1 Sep 2000 Cross Ref Rational function fits to the nonresonant elastic differential cross sections (DCS) for e + He collisions, 0°–180°, 0.1 to 1000 eVAtomic Data and Nuclear Data Tables, Vol. 52, No. 1 | 1 Sep 1992 Cross Ref Functional ApproximationHandbook of Applied Mathematics | 1 Jan 1990 Cross Ref A Modified Remes AlgorithmSIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 6 | 13 July 2006AbstractPDF (1547 KB)Stability of the linear inequality method for rational Chebyshev approximationJournal of Computational and Applied Mathematics, Vol. 11, No. 2 | 1 Oct 1984 Cross Ref An Application of a Restricted Range Version of the Differential Correction Algorithm to the Design of Digital SystemsNumerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory | 1 Jan 1976 Cross Ref Synthesis of spectrum shaping digital filters of recursive designIEEE Transactions on Circuits and Systems, Vol. 22, No. 3 | 1 Mar 1975 Cross Ref Computational Methods in Special Functions-A SurveyTheory and Application of Special Functions | 1 Jan 1975 Cross Ref Best rational product approximations of functions. 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