A bandhyphen;Lanczos method for computing matrix elements of a resolvent

摘要

The bandhyphen;Lanczos algorithm is used to compute a few matrix elements of a resolvent, i.e., to compute lang;psgr;kVerbar;(ohgr;minus;H)minus;1Verbar;psgr;lrang;. HereHdenotes a Hermitian matrix of large dimension. It is shown that the proposed method which is based on the bandhyphen;Lanczos algorithm is more efficient than a method based on simplehyphen;Lanczos algorithm, e.g., than the residue algebra method. The performance of the Lanczos algorithm (both simple and band) for evaluating resolvents or other functions ofHis discussed in some detail.