We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from theâ€¦ (More)

This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of softwareâ€¦ (More)

In this note we present a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v and establish a priori and a posteriori error estimates. Several suchâ€¦ (More)

This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into twoâ€¦ (More)

We describe several methods based on combinations of Krylov subspace techniques, deation procedures and preconditionings, for computing a small number of eigenvalues and eigenvectors or Schur vectorsâ€¦ (More)

In this paper we propose a few methods for solving large Lyapunov equations that arise in control problems. We consider the common case where the right hand side is a small rank matrix. For theâ€¦ (More)

The present paper deals with the problem of computing a few of the eigenvalues with largest (or smallest) real parts, of a large sparse nonsymmetric matrix. We present a general accelerationâ€¦ (More)

This paper gives an overview of projection methods based on Krylov subspaces with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylovâ€¦ (More)