Error Bounds for Sturm-Liouville Eigenvalue Approximations by Several Piecewise Cubic Rayleigh-Ritz Methods
Olin G. Johnson · SIAM Journal on Numerical Analysis · 1969
Next article Error Bounds for Sturm-Liouville Eigenvalue Approximations by Several Piecewise Cubic Rayleigh-Ritz MethodsOlin G. JohnsonOlin G. Johnsonhttps://doi.org/10.1137/0706030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff, , C. de Boor, , B. Swartz and , B. Wendroff, Rayleigh-Ritz approximation by piecewise cubic polynomials, SIAM J. Numer. Anal., 3 (1966), 188–203 10.1137/0703015 MR0203926 0143.38002 LinkGoogle Scholar[2] P. G. Ciarlet, , M. H. Schultz and , R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem, Numer. Math., 9 (1966/1967), 394–430 10.1007/BF02162155 MR0221761 0155.20403 CrossrefISIGoogle Scholar[3] P. G. Ciarlet, , M. H. Schultz and , R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. III. Eigenvalue problems, Numer. Math., 12 (1968), 120–133 10.1007/BF02173406 MR0233517 0181.18303 CrossrefISIGoogle Scholar[4] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963, 69–75 MR0157156 0111.06003 Google Scholar[5] C. C. Farrington, , R. T. Gregory and , A. H. Taub, On the numerical solution of Sturm-Liouville differential equations, Math. Tables Aids Comput., 11 (1957), 131–150 MR0090127 0083.12103 CrossrefGoogle Scholar[6] N. A. Tikhonov and , A. A. Samarskii, The Sturm-Liouville difference problem, U.S.S.R. Comput. Math. and Math. Phys., 4 (1962), 939–961 10.1016/0041-5553(62)90022-8 MR0193761 CrossrefGoogle Scholar[7] Burton Wendroff, Bounds for eigenvalues of some differential operators by the Rayleigh-Ritz method, Math. Comp., 19 (1965), 218–224 MR0179932 0139.10703 CrossrefISIGoogle Scholar[8] Burton Wendroff, Theoretical numerical analysis, Academic Press, New York, 1966, 96–109 MR0196896 0141.32805 Google Scholar Next article FiguresRelatedReferencesCited ByDetails The relative error in the Pruess method for Sturm–Liouville problemsLinear Algebra and its Applications, Vol. 309, No. 1-3 | 1 Apr 2000 Cross Ref ReferencesHandbook of Splines | 1 Jan 1999 Cross Ref Reliability of one-dimensional Dirichlet wave functionsPhysical Review A, Vol. 51, No. 6 | 1 June 1995 Cross Ref NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS: SURVEY AND SOME RECENT RESULTS ON DIFFERENCE METHODSNumerical Solutions of Boundary Value Problems for Ordinary Differential Equations | 1 Jan 1975 Cross Ref On the use of singular functions with finite element approximationsJournal of Computational Physics, Vol. 13, No. 2 | 1 Oct 1973 Cross Ref Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential EquationSteven PruessSIAM Journal on Numerical Analysis, Vol. 10, No. 1 | 14 July 2006AbstractPDF (1084 KB)Higher order convergence results for the Rayleigh-Ritz method applied to eigenvalue problems: 2. Improved error bounds for eigenfunctionsNumerische Mathematik, Vol. 19, No. 2 | 1 Apr 1972 Cross Ref Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to EigenfunctionsJ. G. Pierce and R. S. VargaSIAM Journal on Numerical Analysis, Vol. 9, No. 1 | 1 August 2006AbstractPDF (1249 KB)Chapter 11 Convergence and Error BoundsThe Method of Weighted Residuals and Variational Principles - With Application in Fluid Mechanics, Heat and Mass Transfer | 1 Jan 1972 Cross Ref Numerical properties of the Ritz-Trefftz algorithm for optimal controlCommunications of the ACM, Vol. 14, No. 6 | 1 Jun 1971 Cross Ref Error Bounds of High Order Accuracy for the State Regulator Problem via Piecewise Polynomial ApproximationsW. E. Bosarge, Jr and O. G. JohnsonSIAM Journal on Control, Vol. 9, No. 1 | 18 July 2006AbstractPDF (1089 KB)THE PAPERSMathematical Software | 1 Jan 1971 Cross Ref Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis317-522 History Submitted:21 August 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706030Article page range:pp. 317-333ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics