Next: Subspace Iteration Up: Single- and Multiple-Vector Iterations Previous: Power Method   Contents   Index

## Inverse Iteration

Inverse iteration, described in Algorithm 4.2, can also be used to solve the NHEP without any apparent change.

As in the Hermitian case, assume that and are an eigenvalue and eigenvector pair of so that is the largest eigenvalue of in magnitude. The inverse power method converges if the starting vector is not perpendicular to . The convergence rate is , where is an eigenvalue of such that is the second largest eigenvalue of in magnitude.

In general, inverse iteration tends to have much more rapid convergence than the power method if is chosen to be very close to a desired eigenvalue. However, inverse iteration does require a factorization of the matrix , making it less attractive when this factorization is expensive.

Susan Blackford 2000-11-20