In this paper, we consider the Schur complement of a subtransformation of a linear transformation defined on the product of two finite dimensional real Hilbert spaces, and in particular, on two Euclidean Jordan algebras. We study complementarity properties of linear transformations that are inherited by principal subtransformations, principal pivot transformations, and Schur complements.

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

This paper discusses the Schur complement viewpoint when developing parallel preconditioners for general sparse linear systems. Schur complement methods are pervasive in numerical linear algebra where they represent a canonical way of implementing divide-and-conquer principles. The goal of this note is to give a brief overview of recent progress made in using these techniques for solving genera...

The standard Schur complement equation based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal solutions are sometimes not attainable. Based on the eigenvalue decomposition of the (1, 1) block of the augmented equation, a reduced augmented equatio...

We present a fraction-free approach to the computation of matrix Pad e systems. The method relies on determining a modiied Schur complement for the coeecient matrices of the linear systems of equations that are associated to matrix Pad e approximation problems. By using this modiied Schur complement for these matrices we are able to obtain a hybrid fraction-free algorithm for their computation....

BACKGROUND The inverse problem of fluorescent molecular tomography (FMT) often involves complex large-scale matrix operations, which may lead to unacceptable computational errors and complexity. In this research, a tree structured Schur complement decomposition strategy is proposed to accelerate the reconstruction process and reduce the computational complexity. Additionally, an adaptive regula...

In the first part of the article we introduce C-algebras associated to self-similar groups and study their properties and relations to known algebras. The algebras are constructed as sub-algebras of the Cuntz-Pimsner algebra (and its homomorphic images) associated with the self-similarity of the group. We study such properties as nuclearity, simplicity and Morita equivalence with algebras relat...

It is well-known that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant, too. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too. Recent research showed that the same type of statement holds for some special subclasses of H-matrices, see, for example, Liu et al. (2004). The aim of this paper is twofold: first, to show that...

We develop an overlapping block preconditioner based on an additive Schwarz method for preconditioning the system of equations arising from discretizing the shallow water equations using the spectral ocean element method approach. The system is complicated by being sparse, but having a very large number of nonzeroes in any row of the matrix, which is never stored. The resulting coupled system o...

In this paper we consider new upscaling and homogenization methods for the pressure equation that are less sensitive to the boundary condition assumptions than many other published methods. We start from the discretized pressure equation and rely on the construction of subproblems with signii-cantly fewer unknowns, describing the behaviour of the solution of the ne-grid problem in suitable subs...