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 …
Harnessing GPU tensor cores for fast FP16 arithmetic to speed up mixed-precision iterative refinement solvers
Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing
applications, especially those in artificial intelligence. Here, we present an investigation …
applications, especially those in artificial intelligence. Here, we present an investigation …
[图书][B] Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics
H Elman, D Silvester, A Wathen - 2014 - books.google.com
This book is a description of why and how to do Scientific Computing for fundamental
models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is …
models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is …
[图书][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 …
presentation of some of the most powerful preconditioning methods for solving finite element …
AmgX: A library for GPU accelerated algebraic multigrid and preconditioned iterative methods
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 …
computational fluid dynamics and oil reservoir simulation. In realistic cases the matrices are …
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 …
for the solution of symmetric and nonsymmetric linear systems of equations, as well as for …
Accelerating scientific computations with mixed precision algorithms
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 …
as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating …
[图书][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 …
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
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 …
equations in electromagnetism. From a linear algebra point of view, this leads to the solution …
Equivalent operator preconditioning for elliptic problems
O Axelsson, J Karátson - Numerical Algorithms, 2009 - Springer
The numerical solution of linear elliptic partial differential equations most often involves a
finite element or finite difference discretization. To preserve sparsity, the arising system is …
finite element or finite difference discretization. To preserve sparsity, the arising system is …