Thick restarting of the Davidson method: An extension to implicit restarting
- Univ. of Minnesota, Minneapolis, MN (United States)
The solution of the large, sparse, eigenvalue problem Ax = {lambda}x, for a few eigenpairs is central to many scientific applications. The Arnoldi method, and its equivalent in the symmetric case the Lanczos method, have been the traditional approach to solving these problems. Preconditioning, through some shift-and-invert technique, is frequently employed, because of the difficulty of these problems. A different approach is followed by the Generalized Davidson (GD) method which is a popular preconditioned variant of the Lanczos iteration. Instead of using a three-term recurrence to build an orthonormal basis for the Krylov subspace, the GD algorithm obtains the next basis vector by explicitly orthogonalizing the preconditioned residual (M - {lambda}I){sup -1} (A - {lambda}I)x against the existing basis. A straightforward extension to the non-symmetric case has also been studied in. The GD method can be regarded as a way of improving convergence and robustness at the expense of a more complicated step.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 433406
- Report Number(s):
- CONF-9604167--Vol.1; ON: DE96015306; CNN: Grant ASC 95-04038; Grant DMR-95 25885
- Country of Publication:
- United States
- Language:
- English
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