The relative error in the Pruess method for Sturm-Liouville problems

Sturm-Liouville theory (34B24) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Cites Work

Correction of Numerov's eigenvalue estimates
On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions
Correction of finite element estimates for Sturm-Liouville eigenvalues
A new look at the Lanczos algorithm for solving symmetric systems of linear equations
On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
On one-parameter unitary groups in Hilbert space
On the accuracy of finite difference approximations to the eigenvalues of differential and integral operators
Numerical methods of high-order accuracy for nonlinear boundary value problems. III: Eigenvalue problems, IV: Periodic boundary conditions
Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods
Higher order convergence results for the Rayleigh-Ritz method applied to eigenvalue problems. I: Improved error bounds for eigenfunctions
Uniform estimation of the eigenvalues of Sturm–Liouville problems
Jacobi’s Method is More Accurate than QR
Higher Order Convergence Results for the Rayleigh–Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh–Ritz and Galerkin Approximations to Eigenfunctions
A NOTE ON THE RELATIVE ERROR FOR THE EIGENVALUES OF THE STURM-LIOUVILLE PROBLEM
Bounds for Eigenvalues of Some Differential Operators by the Rayleigh-Ritz Method
Rayleigh-Ritz Approximation by Piecewise Cubic Polynomials
Error Bounds for Sturm-Liouville Eigenvalue Approximations by Several Piecewise Cubic Rayleigh-Ritz Methods
On the speed of convergence of approximate methods in the eigenvalue problem
Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation
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