Thick-restart Lanczos method for electronic structure calculations

This paper describes two recent innovations related to the restarted Lanczo s method for eigenvalue problems, namely the thick-restart technique and dy namic restarting schemes. Previous restarted versions of the Lanczos method use considerably more iterations than the non-restarted versions, largely because too much information is discarded during restarting. The thick-rest art technique provides a mechanism to preserve a large portion of the exist ing basis and dynamic restarting schemes decide exactly how many vectors to save. Combining these two new techniques we are able to implement an effic ient eigenvalue problem solver. This paper will demonstrate its effectivene ss on one particular class of problems for which this method is well suited : linear eigenvalue problems generated from non-selfconsistent electronic s tructure calculations. (C) 1999 Academic Press.