The Lanczos Algorithm with Implicit Deflation.

The simple Lanczos process is very effective for finding a few extreme eigenvalues of a large symmetric matrix along with the associated eigenvectors. Unfortunately the process computes redundant copies of the outermost eigenvectors and has to be used with some skill. In this paper it is shown how a modification called implicit deflation stifles the formation of duplicate eigenvectors without increasing the cost of a Lanczos step significantly. The degree of linear independence among the Lanczos vectors is controlled without the costly process of reorthogonalization. Author