A Comparison of the Successive Overrelaxation Method and Semi-Iterative Methods Using Chebyshev Polynomials

Abstract

Next article A Comparison of the Successive Overrelaxation Method and Semi-Iterative Methods Using Chebyshev PolynomialsRichard S. VargaRichard S. Vargahttps://doi.org/10.1137/0105004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation, 4 (1950), 65–75 MR0046149 CrossrefGoogle Scholar[2] Cornelius Lanczos, Solution of systems of linear equations by minimized-iterations, J. Research Nat. Bur. Standards, 49 (1952), 33–53 MR0051583 CrossrefISIGoogle Scholar[3] E. Stiefel, On solving Fredholm integral equations. Applications to conformal mapping and variational problems of potential theory, J. Soc. Indust. Appl. Math., 4 (1956), 63–85 10.1137/0104005 MR0087226 0072.33505 LinkISIGoogle Scholar[4] E. L. Wachspress, Iterative methods for solving elliptic-type differential equations with application to two-space-dimension multi-group analysis, Knolls Atomic Power Laboratory Report 1333, 1955 Google Scholar[5] J. Wedderburn, Lectures on matrices, Amer. Math. Soc. Colloquium Publications, Vol. 17, New York, 1934 0010.09904 CrossrefGoogle Scholar[6] 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[7] David Young, On Richardson's method for solving linear systems with positive definite matrices, J. Math. Physics, 32 (1954), 243–255 MR0060306 0055.11202 CrossrefISIGoogle Scholar[8] David Young, On the solution of linear systems by iteration, Proceedings of Symposia in Applied Mathematics. Vol. VI. Numerical analysis, McGraw-Hill Book Company, Inc., New York for the American Mathematical Society, Providence, R. I., 1956, 283–298 MR0081539 0071.11801 Google Scholar[9] Richard H. Stark, Rates of convergence in numerical solution of the diffusion equation, J. Assoc. Comput. Mach., 3 (1956), 29–40 MR0074931 CrossrefISIGoogle Scholar[10] Richard S. Varga, Numerical solution of the two-group diffusion equation in $x-y$ geometry, Trans. I. R. E., NS-4 (1957), 52–62 MR0102922 Google Scholar Next article FiguresRelatedReferencesCited byDetails Multigrid Convergence for Discretizations of Singular Perturbation Problems with Grid-Aligned FlowJames S. Otto12 July 2006 | SIAM Journal on Numerical Analysis, Vol. 33, No. 1AbstractPDF (1859 KB)Optimal Equivalent PreconditionersThomas Manteuffel and James Otto1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 30, No. 3AbstractPDF (2332 KB)Acceleration of Relaxation Methods for Non-Hermitian Linear SystemsM. Eiermann, W. Niethammer, and R. S. Varga17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 3AbstractPDF (1226 KB)On Hybrid Semi-Iterative MethodsM. Eiermann, X. Li, and R. S. Varga14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 26, No. 1AbstractPDF (1613 KB)Error Bounds for the SSOR Semi-Iterative MethodLala B. Krishna3 August 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 6, No. 2AbstractPDF (380 KB)On the Convergence of Some Generalized Preconditioned Iterative MethodsNikolaos M. Missirlis and David J. Evans17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 18, No. 4AbstractPDF (565 KB)On the Equivalence of Certain Iterative Acceleration MethodsL. A. Hageman, Franklin T. Luk, and David M. Young17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 17, No. 6AbstractPDF (2175 KB)On Complex Second-Degree Iterative MethodsDavid R. Kincaid14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 11, No. 2AbstractPDF (739 KB)A Survey of Modern Numerical AnalysisDavid M. Young2 August 2006 | SIAM Review, Vol. 15, No. 2AbstractPDF (2464 KB) Volume 5, Issue 2| 1957Journal of the Society for Industrial and Applied Mathematics History Submitted:03 October 1956Published online:10 July 2006 InformationCopyright © 1957 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0105004Article page range:pp. 39-46ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics