The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up hundreds of millions or even tens billions. computational cost using any is dominated by the number sparse matrix-vector multiplications required reach suitable convergence. Block replaces multiplication matrix-matrix multiplication; multplication more efficient, due improved data ...

Over the past decade considerable progress has been made towards the numerical solution of large-scale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million variables can be solved. The methods and software that have led to these advances are surveyed.

The construction of a closed-loop observer for linear control systems and the associated eigenvalue assignment problem are classical tasks in Control Theory. The present paper describes an algorithm for the solution of this eigenvalue assignment problem. The algorithm is based on the implicitly restarted Arnoldi method, and is well suited for large-scale problems, that require the (re)assignmen...

This paper surveys techniques for calculating eigenvalues and eigenvectors of very large matrices.