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 …

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 …

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 …

Progress in numerical weather and climate prediction accuracy greatly depends on the
growth of the available computing power. As the number of cores in top computing facilities …

Contemporary large-scale Partial Differential Equation (PDE) simulations usually require the
solution of large and sparse linear systems. Moreover, it is often needed to solve these …

In this paper, we analyze all possible situations of rank deficiency that cause breakdown in
block conjugate gradient (BCG) solvers. A simple solution, breakdown-free block conjugate …

The restarted block generalized minimum residual method (BGMRES) with deflated
restarting (BGMRES‐DR) was proposed by Morgan to dump the negative effect of small …

We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et
al. SISC 2005], which is an iterative method allowing for the efficient minimization of the the …

We consider the efficient solution of linear systems with multiple shifts and multiple right-
hand sides given simultaneously that arise frequently in large-scale scientific and …

Abstract We describe Parallel-Projection Block Conjugate Gradient (pp-bcg), a distributed
iterative solver for the solution of dense and symmetric positive definite linear systems with …