Jacobi-Davidson Methods

The Lanczos method (see §4.4) is quite effective in computing eigenvalues in the ends of the spectrum of if these eigenvalues are well separated from the remaining spectrum, or if it is applied to a shifted and inverted matrix operator , for some reasonable shift close to the interesting eigenvalues.

If none of these conditions is fulfilled, for instance, if the computation of a vector for given is not feasible with a direct solver, then variants of the Jacobi-Davidson method [411] offer an attractive alternative.

- Basic Theory
- Basic Algorithm
- Restart and Deflation
- Computing Interior Eigenvalues
- Software Availability
- Numerical Example

Susan Blackford 2000-11-20