Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to Eigenfunctions

DOI10.1137/0709014zbMath0301.65063OpenAlexW2056630064MaRDI QIDQ4055108

Publication date: 1972

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0709014

Mathematics Subject Classification ID

Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (18)

General solution theory for Schrödinger's equation in arbitrary 2D- periodic spatial structures. I: The monolayer problem ⋮ Optimal nonlinear transformations of random variables ⋮ The relative error in the Pruess method for Sturm-Liouville problems ⋮ Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas ⋮ Some projection methods for the eigenvalue problem ⋮ Exploring the statistical applicability of the Poincaré inequality: a test of normality ⋮ La méthode de Rayleigh Ritz appliquee à des opérateurs différentiels elliptiques - ordre de convergence des éléments propres ⋮ Approximation of the eigenvectors of a positive compact operator and estimate of the error ⋮ A mixed finite element method for the biharmonic eigenvalue problems of plate bending ⋮ Diskrete Approximation von Eigenwertproblemen. I: Qualitative Konvergenz ⋮ Diskrete Approximation von Eigenwertproblemen. II: Konvergenzordnung ⋮ On the order of convergence of finite element approximations to eigenvalues and eigenfunctions ⋮ Convergence of the Rayleigh-Ritz method for eigenvalue problems. ⋮ Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations ⋮ Higher order convergence results for the Rayleigh-Ritz method applied to eigenvalue problems. I: Improved error bounds for eigenfunctions ⋮ Eigenvalue approximation by the finite element method ⋮ Finite element interpolation error bounds with applications to eigenvalue problems ⋮ Finite elements for the eigenvalue problem of differential operators in unbounded intervals

This page was built for publication: Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to Eigenfunctions