Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …

This article surveys preconditioning techniques for the iterative solution of large linear
systems, with a focus on algebraic methods suitable for general sparse matrices. Covered …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

In this paper, we analyze the main features and discuss the tuning of the algorithms for the
direct solution of sparse linear systems on distributed memory computers developed in the …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

Discretization of linear inverse problems generally gives rise to very ill-conditioned linear
systems of algebraic equations. Typically, the linear systems obtained have to be …

A comparison study of the efficiency and accuracy of a variety of meshless trial and test
functions is presented in this paper, based on the general concept of the meshless local …

MUMPS is a public domain software package for the multifrontal solution of large sparse
linear systems on distributed memory computers. The matrices can be symmetric positive …

This document describes a collection of three related ANSI C subroutine libraries for solving
sparse linear systems of equations AX= B. Here A is a square, nonsingular, nxn sparse …

A new method for sparse LU factorization is presented that combines a column pre-ordering
strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The …