Journal Article10.1137/S0036144599363084
A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems
TL;DR: A new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors is proposed that has improved convergence properties and that may be used for general matrices.
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Abstract: In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi's approach, combined with Davidson's method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.
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TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
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The Symmetric Eigenvalue Problem
Beresford N. Parlett
- 01 Jan 1980
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.7K
The Symmetric Eigenvalue Problem.
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.4K