GMRES algorithms over 35 years

Q Zou - Applied Mathematics and Computation, 2023 - Elsevier
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 …

A survey of subspace recycling iterative methods

KM Soodhalter, E de Sturler, ME Kilmer - GAMM‐Mitteilungen, 2020 - Wiley Online Library
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 …

Krylov methods for nonsymmetric linear systems

G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
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 …

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

T Benacchio, L Bonaventura… - … Journal of High …, 2021 - journals.sagepub.com
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 …

Block iterative methods and recycling for improved scalability of linear solvers

P Jolivet, PH Tournier - SC'16: Proceedings of the International …, 2016 - ieeexplore.ieee.org
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 …

A breakdown-free block conjugate gradient method

H Ji, Y Li - BIT Numerical Mathematics, 2017 - Springer
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 …

A block GMRES method with deflated restarting for solving linear systems with multiple shifts and multiple right‐hand sides

DL Sun, TZ Huang, YF Jing… - … Linear Algebra with …, 2018 - Wiley Online Library
The restarted block generalized minimum residual method (BGMRES) with deflated
restarting (BGMRES‐DR) was proposed by Morgan to dump the negative effect of small …

A block recycled GMRES method with investigations into aspects of solver performance

ML Parks, KM Soodhalter, DB Szyld - arXiv preprint arXiv:1604.01713, 2016 - arxiv.org
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 …

A new shifted block GMRES method with inexact breakdowns for solving multi-shifted and multiple right-hand sides linear systems

DL Sun, TZ Huang, B Carpentieri, YF Jing - Journal of Scientific Computing, 2019 - Springer
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 …

A scalable iterative dense linear system solver for multiple right-hand sides in data analytics

V Kalantzis, ACI Malossi, C Bekas, A Curioni… - Parallel Computing, 2018 - Elsevier
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 …