Drawing analogies with block spin techniques used to study continuum limits in critical phenomena, we attempt to block up D-branes by averaging over near neighbour elements of their (in general noncommuting) matrix coordinates, i.e. in a low energy description. We show that various D-brane (noncommutative) geometries arising in string theory appear to behave sensibly under blocking up, given ce...

In this paper we consider numerical solution of 3D linear elasticity equations described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. Preconditioned Conjugate Gradient iterative method is used for solving large-scale linear algebraic systems arising after the Finite Element Method (FEM) dis...

In this paper we consider the parallel generalized SAOR iterative method based on the generalized AOR iterative method presented by James for solving large nonsingular system. We obtain some convergence theorems for the case when coefficient matrix is a block diagonally dominant matrix or a generalized block diagonal dominant matrix. A numerical example is given to illustrate to our results. Cr...

Bordered almost block diagonal systems arise from discretizing a linearized rst-order system of n ordinary diierential equations in a two-point boundary value problem with non-separated boundary conditions. The discretization may use spline collocation, nite diierences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standa...

This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of a sparse matrix. The first uses a divide-and-conquer principle and the ShermanMorrison-Woodbury formula, and assumes that the matrix can be decomposed into a 2 × 2 block-diagonal matrix and a low-rank matrix. The second method is a standard domain decomposition approach in which...

For the simulation and optimization of large scale chemical processes, the overall computing time is often dominated by the time needed to solve a large sparse system of linear equations. A parallel frontal solver can be used to signi cantly reduce the wallclock time required to solve these linear equation systems using parallel/vector supercomputers. This is done by exploiting both multiproces...

The block diagonalization (BD) is a linear precoding technique for multi-user multi-input multi-output (MIMO) broadcast channels, which is able to completely eliminate the multi-user interference (MUI), but it is not computationally efficient. In this paper, we propose the block diagonal Jacket matrix decomposition, which is able not only to extend the conventional block diagonal channel decomp...

Block diagonal preconditioners for the mixed finite element formulation of planar linear elasticity using the PEERS element by Arnold, Brezzi and Douglas [1] are studied. This mixed finite element approach treats the stress tensor, the displacement field and the anti-symmetric part of the strain tensor as independent variables. The resulting linear system of equations is symmetric but indefinit...

We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...

This paper presents a systematic theoretical and numerical evaluation of three common block preconditioners in a Krylov subspace method for solving symmetric indefinite linear systems. The focus is on large-scale real world problems where block approximations are a practical necessity. The main illustration is the performance of the block diagonal, constrained, and lower triangular precondition...