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 …

Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing
applications, especially those in artificial intelligence. Here, we present an investigation …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …