Accuracy of Rayleigh- Ritz Approximations
نویسندگان
چکیده
New bounds on the canonical angles between an invariant subspace of A and an approximating subspace by the differences between Ritz values and the targeted eigenvalues are obtained. From this result, various bounds are readily available to estimate how accurate the Ritz vectors computed from the approximating subspace may be, based on information on approximation accuracies in the Ritz values. The result is helpful in understanding how Ritz vectors move towards eigenvectors while Ritz values are made to move towards eigenvalues.
منابع مشابه
Majorization Bounds for Ritz Values of Hermitian Matrices∗
Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...
متن کاملElectronic Transactions on Numerical Analysis
Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...
متن کاملVibration Analysis for Rectangular Plate Having a Circular Central Hole with Point Support by Rayleigh-Ritz Method
In this paper, the transverse vibrations of rectangular plate with circular central hole have been investigated and the natural frequencies of the mentioned plate with point supported by Rayleigh-Ritz Method have been obtained. In this research, the effect of the hole is taken into account by subtracting the energies of the hole domain from the total energies of the whole plate. To determine th...
متن کاملThe Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs
We extend the Rayleigh–Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectorsmay fail to converge. To overcome this potential pr...
متن کاملOn Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems
This paper deals with the computation of the eigenvalues of a three-parameter Sturm-Liouville problem in the form of ordinary differential equation using Rayleigh-Ritz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues of self-adjoint problems. The resulting equations obtained in applying Rayleigh-Ritz method on t...
متن کامل