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 …

Abstract Electrical Impedance Tomography (EIT) is a recently developed imaging technique.
Small insensible currents are injected into the body using electrodes. Measured voltages …

This paper analyzes dropping strategies in a multilevel incomplete LU decomposition
context and presents a few strategies for obtaining related ILUs with enhanced robustness …

This paper presents an efficient implementation of the incomplete LU (ILU) factorization
derived from the Crout version of Gaussian elimination. At step k of the elimination, the k th …

Large sparse linear systems of equations are ubiquitous in science, engineering and
beyond. This open access monograph focuses on factorization algorithms for solving such …

We describe a novel technique for computing a sparse incomplete factorization of a general
symmetric positive definite matrix A. The factorization is not based on the Cholesky algorithm …

In this paper we consider the problem of preconditioning symmetric positive definite matrices
of the form A α= A+ α I where α> 0. We discuss how to cheaply modify an existing sparse …

An incomplete LU decomposition with pivoting is presented that progressively monitors the
growth of the inverse factors of L, U. The information on the growth of the inverse factors is …

In this paper we present a new ILU decomposition which is based on an existing sparse
direct solver. In contrast to many incomplete LU decompositions this ILU incorporates …

This paper discusses some relationships between ILU factorization techniques and factored
sparse approximate inverse techniques. While ILU factorizations compute approximate LU …