This paper sketches the main research developments in the area of iterative methods for
solving linear systems during the 20th century. Although iterative methods for solving linear …

The purpose of this book is to unify and document in one place many of the techniques and
much of the current understanding about solving systems of linear equations on vector and …

In this chapter, we give a brief overview of a particular class of preconditioners known as
incomplete factorizations. They can be thought of as approximating the exact LU …

Knowledge of fluid pressure is important to predict the presence of oil and gas in reservoirs.
A mathematical model for the prediction of fluid pressures is given by a time-dependent …

We investigate here rounding error effects on the convergence rate of the conjugate
gradients. More precisely, we analyse on both theoretical and experimental basis how finite …

Preconditioning techniques based on incomplete factorization of matrices are investigated,
to solve highly indefinite complex‐symmetric linear systems. A novel preconditioning is …

In this paper a multilevel-like ILU preconditioner is introduced. The ILU factorization
generates its own ordering during the elimination process. Both ordering and dropping …

We present a new supernode-based incomplete LU factorization method to construct a
preconditioner for solving sparse linear systems with iterative methods. The new algorithm is …

The solution of dense linear systems received much attention after the second world war,
and by the end of the sixties, most of the problems associated with it had been solved. For a …

We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on
the conjugate gradient algorithm with incomplete factorization preconditioning, using a …