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 …

[BOOK][B] Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics

HC Elman, DJ Silvester, AJ Wathen - 2014 - books.google.com
This book describes why and how to do Scientific Computing for fundamental models of fluid
flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely …

Harnessing GPU tensor cores for fast FP16 arithmetic to speed up mixed-precision iterative refinement solvers

A Haidar, S Tomov, J Dongarra… - … Conference for High …, 2018 - ieeexplore.ieee.org
Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing
applications, especially those in artificial intelligence. Here, we present an investigation …

[BOOK][B] Multilevel block factorization preconditioners: Matrix-based analysis and algorithms for solving finite element equations

PS Vassilevski - 2008 - books.google.com
This monograph is the first to provide a comprehensive, self-contained and rigorous
presentation of some of the most powerful preconditioning methods for solving finite element …

Theory of inexact Krylov subspace methods and applications to scientific computing

V Simoncini, DB Szyld - SIAM Journal on Scientific Computing, 2003 - SIAM
We provide a general framework for the understanding of inexact Krylov subspace methods
for the solution of symmetric and nonsymmetric linear systems of equations, as well as for …

AmgX: A library for GPU accelerated algebraic multigrid and preconditioned iterative methods

M Naumov, M Arsaev, P Castonguay, J Cohen… - SIAM Journal on …, 2015 - SIAM
The solution of large sparse linear systems arises in many applications, such as
computational fluid dynamics and oil reservoir simulation. In realistic cases the matrices are …

Accelerating scientific computations with mixed precision algorithms

M Baboulin, A Buttari, J Dongarra, J Kurzak… - Computer Physics …, 2009 - Elsevier
On modern architectures, the performance of 32-bit operations is often at least twice as fast
as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating …

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

A Haidar, H Bayraktar, S Tomov… - … of the Royal …, 2020 - royalsocietypublishing.org
Double-precision floating-point arithmetic (FP64) has been the de facto standard for
engineering and scientific simulations for several decades. Problem complexity and the …

[BOOK][B] The Lanczos and conjugate gradient algorithms: from theory to finite precision computations

G Meurant - 2006 - SIAM
The Lanczos algorithm is one of the most frequently used numerical methods for computing
a few eigenvalues (and eventually eigenvectors) of a large sparse symmetric matrix A. If the …

Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations

B Carpentieri, IS Duff, L Giraud, G Sylvand - SIAM Journal on Scientific …, 2005 - SIAM
The boundary element method has become a popular tool for the solution of Maxwell's
equations in electromagnetism. From a linear algebra point of view, this leads to the solution …