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 …

When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

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 …

This book describes why and how to do Scientific Computing for fundamental models of fluid
flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely …

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 …

We have observed that the residual vectors at the end of each restart cycle of restarted
GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We …

In [M. Benzi and MA Olshanskii, SIAM J. Sci. Comput., 28 (2006), pp. 2095--2113] a
preconditioner of augmented Lagrangian type was presented for the two-dimensional …

Restricted Denominator (RD) rational approximations to the matrix exponential operator are
constructed by interpolation in points related to Krylov subspaces associated to a rational …

Given an oblique projector P on a Hilbert space, ie, an operator satisfying P 2= P, which is
neither null nor the identity, it holds that|| P||=|| I–P||. This useful equality, while not widely …

Flexible Krylov methods refers to a class of methods which accept preconditioning that can
change from one step to the next. Given a Krylov subspace method, such as CG, GMRES …