This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Abstract Block Gram-Schmidt algorithms serve as essential kernels in many scientific
computing applications, but for many commonly used variants, a rigorous treatment of their …

This survey concerns subspace recycling methods, a popular class of iterative methods that
enable effective reuse of subspace information in order to speed up convergence and find …

We consider deflation and augmentation techniques for accelerating the convergence of
Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

A variety of block Krylov subspace methods have been successfully developed for linear
systems and matrix equations. The application of block Krylov methods to compute matrix …

In this paper, we present a comprehensive framework for studying Krylov subspace methods
used to solve the linear system A x= f. These methods aim to achieve convergence within a …

A restarted Arnoldi algorithm is given that computes eigenvalues and eigenvectors. It is
related to implicitly restarted Arnoldi, but has a simpler restarting approach. Harmonic and …

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly
also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by …

We consider the solution of large linear systems with multiple right-hand sides using a block
GMRES approach. We introduce a new algorithm that effectively handles the situation of …