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In [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2347--2359] it was shown that $k$ steps of the finite precision Lanczos process for tridiagonalizing an $n\times n$ Hermitian matrix $A$ could be viewed as an exact Lanczos process for a $(k+n)\times (k+n)$ ...

In a recent paper, Rostami [SIAM J. Sci. Comput, 37 (2015), pp. S447--S471] has presented an interesting algorithm for the computation of the real pseudospectral abscissa and the real stability radius (aka the distance to instability) of a square matrix $A \...

We consider matrix-free solver environments where information about the underlying matrix is available only through matrix vector computations which do not have access to a fully assembled matrix. We introduce the notion of partial matrix ...

The generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869] for solving linear systems Ax=b is implemented as a sequence of least squares problems involving Krylov subspaces of ...

Minimum residual norm iterative methods for solving linear systems Ax=b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige ...

In this paper we introduce a new approach to algebraic multilevel methods and their use as preconditioners in iterative methods for the solution of symmetric positive definite linear systems. The multilevel process and, in particular, the coarsening ...

We describe the design, implementation, and performance of a frontal code for the solution of large, sparse, unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is ...

Arnoldi methods can be more effective than subspace iteration methods for computing the dominant eigenvalues of a large, sparse, real, unsymmetric matrix. A code, EB12, for the sparse, unsymmetric eigenvalue problem based on a subspace iteration ...

This paper discusses the design and development of a code to calculate the eigenvalues of a large sparse real unsymmetric matrix that are the rightmost, leftmost, or are of the largest modulus. A subspace iteration algorithm is used to compute a sequence ...