Preconditioning Eigenvalues and Some Comparison of Solvers

Preconditioning techniques are discussed for symmetric eigenvalue problems. The methods Davidson, Jacobi-Davidson, Rayleigh quotient iteration, and preconditioned Lanczos are considered. Some relationships are given between these different approaches, and some experimental comparisons are done. Jacobi-Davidson appears to be efficient in both expense and storage. A hybrid method may be helpful for the case of a poor initial vector. short running title: Preconditioning Eigenvalues