This article reviews linear instability analysis of flows over or through complex two-
dimensional (2D) and 3D geometries. In the three decades since it first appeared in the …

In this paper we review the state of affairs in the area of approximation of large-scale
systems. We distinguish three basic categories, namely the {SVD}-based, the {Krylov}-based …

In today's technological world, physical and artificial processes are mainly described by
mathematical models, which can be used for simulation or control. These processes are …

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 …

In traditional physicochemical modeling, one derives evolution equations at the
(macroscopic, coarse) scale of interest; these are used to perform a variety of tasks …

In this paper, we study numerical behavior of several computational variants of the Gram-
Schmidt orthogonalization process. We focus on the orthogonality of computed vectors …

This document describes slePc, the Scalable Library for Eigenvalue Problem Computations,
a software package for the solution of large sparse eigenproblems on parallel computers. It …

This paper provides two results on the numerical behavior of the classical Gram-Schmidt
algorithm. The first result states that, provided the normal equations associated with the …

Methods for the approximation of large-scale dynamical systems will be surveyed. There are
mainly two families namely, the SVD-based and Krylov-based approximation methods. The …

In this article we describe our implementations of the GMRES algorithm for both real and
complex, single and double precision arithmetics suitable for serial, shared memory and …