The complement system, through the action of its nine components and various cleavage products, plays a major role in the inflammatory response. In rheumatoid arthritis a depression of total haemolytic complement (Hedberg, 1963, 1964, 1967; Pekin and Zvaifler, 1964; Fostiropoulos, Austen, and Bloch, 1965; Barnett, Bienenstock, and Bloch, 1966; Peltier, Coste, and Delbarre, 1966; Vaughan, Barnet...

A hybrid linear solver based on the Schur complement method has great potential to be a general purpose solver scalable on tens of thousands of processors. For this, it is imperative to exploit two levels of parallelism; namely, solving independent subdomains in parallel and using multiple processors per subdomain. This hierarchical parallelism can lead to a scalable implementation which mainta...

A hybrid linear solver based on the Schur complement method has great potential to be a general purpose solver scalable on tens of thousands of processors. It is imperative to exploit two levels of parallelism; namely, solving independent subdomains in parallel and using multiple processors per subdomain. This hierarchical parallelism can lead to a scalable implementation which maintains numeri...

In this paper we investigate some matrix structures on C that have a good behaviour under Schur complementation. The first type of structure is closely related to low displacement rank matrices. Next, we show that for a matrix having a low rank submatrix, also the Schur complement must have a low rank submatrix, which we can explicitly determine. This property holds even if the low rank submatr...

As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices (a proper subset of H -matrices); that is, we show that the Schur complement of a generalized doubly diagonally dominant matrix is a generaliz...

As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H−matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset α ⊂ {1, 2, . . . , n} so that the Schur complement matrix A/α is an H−matrix. These conditions are then applied to ...

Domain decomposition algorithms have received much attention in the last decade [2]. The domain in which a differential equation is defined is partitioned in several subdomains, and the equation is solved in these domains. The local results are integrated to form the solution in the entire domain. Since the subdomains can be solved in parallel, domain decomposition has become very popular on pa...

Partitioned symmetric matrices, in particular the Hessian of the Lagrangian, play a fundamental role in nonlinear optimization. For this type of matrices S.-P. Han and 0. Fujiwara recently presented an inertia theorem under a certain regularity assumption. We prove that this theorem is true without any regularity assumption. Then we consider matrix extensions preserving the sign of the determin...

We present two new variants of Schur complement domain decomposition preconditioners suitable for 2D anisotropic problems. These variants are based on adaptations of the probing idea 5] used in conjunction with a coarse grid approximation 3]. The new methods are speciically designed for situations when the coupling between neighboring interfaces is stronger than the coupling within an interface...

A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. ...