The Generalized Overrelaxation Method for the Approximate Solution of Operator Equations in Hilbert Space

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Previous article Next article The Generalized Overrelaxation Method for the Approximate Solution of Operator Equations in Hilbert SpaceW. V. PetryshynW. V. Petryshynhttps://doi.org/10.1137/0110052PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Julius Albrecht, Fehlerabschätzungen bei Relaxationsverfahren zur numerischen Auflösung linearer Gleichungssysteme, Numer. Math., 3 (1961), 188–201 10.1007/BF01386019 MR0146957 0111.12602 CrossrefGoogle Scholar[2] Hans Bückner, A special method of successive approximations for Fredholm integral equations, Duke Math. J., 15 (1948), 197–206 MR0025290 0030.39201 CrossrefISIGoogle Scholar[3] Yu. L. Daleckii˘, Integration and differentiation of functions of Hermitian operators depending on a parameter, Uspehi Mat. Nauk (N.S.), 12 (1957), 182–186 MR0086276 Google Scholar[4] W. Dück, Eine Fehlerabschätzung zum Einzelschrittverfahren bei linearen Gleichungssystemen, Numer. Math., 1 (1959), 73–77 MR0102910 0084.34504 CrossrefGoogle Scholar[5A] Gene H. Golub and , Richard S. Varga, Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second order Richardson iterative methods. I, Numer. Math., 3 (1961), 147–156 10.1007/BF01386013 MR0145678 0099.10903 CrossrefGoogle Scholar[5B] Gene H. Golub and , Richard S. Varga, Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second order Richardson iterative methods. II, Numer. Math., 3 (1961), 157–168 10.1007/BF01386014 MR0145679 0099.10903 CrossrefGoogle Scholar[6] G. J. Habetler and , E. L. Wachspress, Symmetric successive overrelaxation in solving diffusion difference equations, Math. Comp., 15 (1961), 356–362 MR0129139 0102.11403 CrossrefGoogle Scholar[7] P. R. Halmos, Introduction to Hilbert space, Chelsea, New York, 1957 0079.12404 Google Scholar[8] Einar Hille and , Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957xii+808 MR0089373 0078.10004 Google Scholar[9] Alston S. Householder, On the convergence of matrix iterations, Rep. ORNL 1883, Oak Ridge National Laboratory, Oak Ridge, Tenn., 1955, 47– MR0075677 Google Scholar[10] H. B. Keller, Numerical Methods, Lecture Notes, New York University, 1959, Ch. 2 Google Scholar[11] A. T. Lonseth, The propagation of error in linear problems, Trans. Amer. Math. Soc., 62 (1947), 193–212 MR0022315 0032.03203 CrossrefISIGoogle Scholar[12] W. V. Petryshyn, Masters Thesis, Direct and Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space, Doctoral Thesis, Columbia University, 1961 Google Scholar[13] Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons Inc., New York, 1958xvi+423 MR0098966 0081.10202 Google Scholar[14] Johannes Weissinger, Verallgemeinerungen des Seidelschen Iterationsverfahrens, Z. Angew. Math. Mech., 33 (1953), 155–163 MR0056375 0050.12401 CrossrefGoogle Scholar[15] G. Wiarda, Integralgleichungen unter besonderer Berücksichtung der Anwendungen, Leipzig, 1930 Google Scholar[16] David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc., 76 (1954), 92–111 MR0059635 0055.35704 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 10, Issue 4| 1962Journal of the Society for Industrial and Applied Mathematics History Submitted:18 January 1962Published online:13 July 2006 InformationCopyright © 1962 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0110052Article page range:pp. 675-690ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics