Abstract
We will discuss iterative methods for the solution of linear large sparse eigenproblems, such as the methods of Lanczos and Arnoldi. In particular, we will pay attention to the recently proposed class of Jacobi-Davidson methods, which represents versatile approaches for the solution of large sparse eigenproblems. In these methods correction equations have to be solved for a proper update of the approximations for an eigenpair. For the solution of these correction equations we may employ the arsenal of techniques available for iterative solution of linear sparse systems, including preconditioning. An overview of variants of the Jacobi-Davidson method for standard linear eigenproblems and generalized eigenproblems will be given. We will also describe how the approach can be used for the efficient computation of a number of eigenpairs.
