Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Summary We present two methods for computing the leading eigenpairs of large sparse unsymmetric matrices. Namely the block-Arnoldi method and an adaptation of the Davidson method to unsymmetric matrices. We give some theoretical results concerning the convergence and discuss implementation aspects of the two methods. Finally some results of numerical tests on a variety of matrices, in which we compare these two methods are reported.