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JACOBI CORRECTION EQUATION, LINE SEARCH, AND CONJUGATE GRADIENTS IN HERMITIAN EIGENVALUE COMPUTATION II: COMPUTING SEVERAL EXTREME EIGENVALUES.
- Source :
-
SIAM Journal on Numerical Analysis . 2008, Vol. 46 Issue 5, p2593-2619. 27p. - Publication Year :
- 2008
-
Abstract
- This paper addresses the question of how to efficiently adapt the conjugate gradient (CG) method to the computation of several leftmost or rightmost eigenvalues and corresponding eigenvectors of Hermitian problems. A generic block CG algorithm instantiated by some available block CG algorithms is considered whereby the new approximate eigenpairs are computed by applying the Rayleigh-Ritz procedure in the trial subspace spanning current approximate eigenvectors and the search direction vectors, each of the latter being a linear combination of the respective gradient of the Rayleigh quotient and all search directions from the previous iteration. An approach related to the so-called Jacobi orthogonal complement correction equation is exploited in the local convergence analysis of this CG algorithm. Based on theoretical considerations, a new block conjugation scheme (a way to compute search directions) is suggested that enjoys a certain kind of optimality and has proved to be competitive in practical eigenvalue computation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 46
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 33227818
- Full Text :
- https://doi.org/10.1137/070688754