Studies on Jacobi–Davidson,Rayleigh quotient iteration,inverse iteration generalized Davidson and Newton updates

We study Davidson‐type subspace eigensolvers. Correction equations of Jacobi–Davidson and several other schemes are reviewed. New correction equations are derived. A general correction equation is constructed, existing correction equations may be considered as special cases of this general equation. The main theme of this study is to identify the essential common ingredient that leads to the efficiency of a diverse form of Davidson‐type methods. We emphasize the importance of the approximate Rayleigh‐quotient‐iteration direction. Copyright © 2006 John Wiley & Sons, Ltd.