Chebyshev Approximation by $a\Pi \frac{{x - r_i }}{{x + s_i }}$ and Application to ADI Iteration
1963; Society for Industrial and Applied Mathematics; Volume: 11; Issue: 1 Linguagem: Inglês
10.1137/0111012
ISSN2168-3484
Autores Tópico(s)Numerical methods in inverse problems
ResumoPrevious article Next article Chebyshev Approximation by $a\Pi \frac{{x - r_i }}{{x + s_i }}$ and Application to ADI IterationCarl de Boor and John R. RiceCarl de Boor and John R. Ricehttps://doi.org/10.1137/0111012PDFPDF PLUSBibTexSections 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] Th. Motzkin, Approximation by curves of a unisolvent family, Bull. Amer. Math. Soc., 55 (1949), 789–793 MR0031111 0034.33302 CrossrefISIGoogle Scholar[3] E. P. Novodvorskii˘ and , I. Š. Pinsker, The process of equating maxima, Uspehi Matem. Nauk (N.S.), 6 (1951), 174–181 MR0046400 Google Scholar[4] John R. Rice, Tchebycheff approximations by functions unisolvent of variable degree, Trans. Amer. Math. Soc., 99 (1961), 298–302 MR0136913 0146.08301 CrossrefGoogle Scholar[5] R. S. Varga, Implicit alternating direction methods, Matrix Iterative Analysis, Prentice-Hall, 1962, chapter 7 Google Scholar[6] Eduard L. C, Numerical methods of Tchebycheff approximation, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, 217–232 MR0107961 0083.35502 Google Scholar[7] E. L. Wachspress and , G. J. Habetler, An alternating-direction-implicit iteration technique, J. Soc. Indust. Appl. Math., 8 (1960), 403–424 10.1137/0108027 MR0114308 0158.33901 LinkISIGoogle Scholar[8] E. L. Wachspress, Optimum alternating-direction-implicit iteration parameters for a model problem, J. Soc. Indust. Appl. Math., 10 (1962), 339–350 10.1137/0110025 MR0150935 0111.31401 LinkISIGoogle Scholar[9] J. L. Walsh, Interpolation and Approximation, Amer. Math. Soc., New York, 1935, chapter 12 0013.05903 Google Scholar[10] H. Maehly and , Ch. Witzgall, Tschebyscheff-Approximationen in kleinen Intervallen. II. Stetigkeitssätze für gebrochen rationale Approximationen, Numer. Math., 2 (1960), 293–307 10.1007/BF01386230 MR0126107 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Application of ADI Iterative Methods to the Restoration of Noisy ImagesSIAM Journal on Matrix Analysis and Applications, Vol. 17, No. 1 | 17 February 2012AbstractPDF (2458 KB)The Direct Solution of the Discrete Poisson Equation on a RectangleSIAM Review, Vol. 12, No. 2 | 18 July 2006AbstractPDF (1273 KB)Tensor Product Analysis of Alternating Direction Implicit MethodsRobert E. Lynch, John R. Rice, and Donald H. ThomasJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4 | 13 July 2006AbstractPDF (1100 KB)Optimum Alternating-Direction-Implicit Iteration Parameters for a Model ProblemE. L. WachspressJournal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2 | 13 July 2006AbstractPDF (961 KB) Volume 11, Issue 1| 1963Journal of the Society for Industrial and Applied Mathematics History Submitted:22 January 1962Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111012Article page range:pp. 159-169ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics
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