Recent computational developments in Krylov subspace methods for linear systems
V Simoncini, DB Szyld - Numerical Linear Algebra with …, 2007 - Wiley Online Library
Many advances in the development of Krylov subspace methods for the iterative solution of
linear systems during the last decade and a half are reviewed. These new developments …
linear systems during the last decade and a half are reviewed. These new developments …
A survey of subspace recycling iterative methods
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 …
enable effective reuse of subspace information in order to speed up convergence and find …
Computing and deflating eigenvalues while solving multiple right-hand side linear systems with an application to quantum chromodynamics
A Stathopoulos, K Orginos - SIAM Journal on Scientific Computing, 2010 - SIAM
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian
positive definite matrix while solving a linear system of equations with conjugate gradient …
positive definite matrix while solving a linear system of equations with conjugate gradient …
Flexible GMRES with deflated restarting
In many situations, it has been observed that significant convergence improvements can be
achieved in preconditioned Krylov subspace methods by enriching them with some spectral …
achieved in preconditioned Krylov subspace methods by enriching them with some spectral …
Block GMRES method with inexact breakdowns and deflated restarting
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 …
GMRES approach. We introduce a new algorithm that effectively handles the situation of …
A survey of low-rank updates of preconditioners for sequences of symmetric linear systems
L Bergamaschi - Algorithms, 2020 - mdpi.com
The aim of this survey is to review some recent developments in devising efficient
preconditioners for sequences of symmetric positive definite (SPD) linear systems A kxk= bk …
preconditioners for sequences of symmetric positive definite (SPD) linear systems A kxk= bk …
On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides
S Gratton, A Sartenaer, J Tshimanga - SIAM Journal on Optimization, 2011 - SIAM
This work studies a class of limited memory preconditioners (LMPs) for solving linear
(positive-definite) systems of equations with multiple right-hand sides. We propose a class of …
(positive-definite) systems of equations with multiple right-hand sides. We propose a class of …
A tensor-train accelerated solver for integral equations in complex geometries
We present a framework using the Quantized Tensor Train (qtt) decomposition to accurately
and efficiently solve volume and boundary integral equations in three dimensions. We …
and efficiently solve volume and boundary integral equations in three dimensions. We …
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 …
solution of large and sparse linear systems. Moreover, it is often needed to solve these …
Three‐dimensional parallel frequency‐domain visco‐acoustic wave modelling based on a hybrid direct/iterative solver
We present a parallel domain decomposition method based on a hybrid direct‐iterative
solver for 3D frequency‐domain modelling of visco‐acoustic waves. The method is …
solver for 3D frequency‐domain modelling of visco‐acoustic waves. The method is …