Thick-Restart Lanczos Method for Electronic Structure Calculations

Abstract

This paper describes two recent innovations related to the restarted Lanczos method for eigenvalue problems, namely the thick-restart technique and dynamic 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-restart technique provides a mechanism to preserve a large portion of the existing basis and dynamic restarting schemes decide exactly how many vectors to save. Combining these two new techniques we are able to implement an efficient eigenvalue problem solver. This paper will demonstrate its effectiveness on one particular class of problems for which this method is well suited: linear eigenvalue problems generated from non-selfconsistent electronic structure calculations.