In the context of the block Cimmino algorithm, we study preprocessing strategies to obtain block partitionings that can be applied to general linear systems of equations Ax = b. We study strategies that transform the matrix AA into a matrix with a block tridiagonal structure. This provides a partitioning of the linear system for row projection methods because block Cimmino is essentially equiva...

in this article, a numerical method based on  improvement of block-pulse functions (ibpfs) is discussed for solving the system of linear volterra and fredholm integral equations. by using ibpfs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. an efficient error estimation and associated theorems for the proposed method are also ...

A new class of error-correcting codes is created from a matrix operation defined within. The matrix operation takes a point-block incidence and produces a new point-block incidence with some desirable properties, including a doubling of the girth of the Tanner graph of the initial matrix. A specific example is created using PG(2, q), and the results are generalized to any point-block incidence ...

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block-tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which freq...

Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

Many of the currently popular \block algorithms" are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

We consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the 1,2 block needs not to equal the transposed 2,1 block, and the 2,2 block may not be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented. The relationship between the two different formulations spectrum of the SIMPL...

where A is a sparse N ×N matrix and v is a dense N -dimensional vector. In parallel, the sparse system is often distributed across np processes such that each process holds a contiguous block of rows from the matrix A, and equivalent rows from the vectors v and w, as shown in Figure 1. A common approach is to also split the rows of A on a single process into two groups: an on-process block, con...

The row-by-row frontal method may be used to solve general large sparse linear systems of equations. By partitioning the matrix into (nearly) independent blocks and applying the frontal method to each block, a coarse-grained parallel frontal algorithm is obtained. The success of this approach depends on preordering the matrix. This can be done in two stages, (1) order the matrix to bordered blo...

In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one may generalize that concept as a block partition of a complex square matrix s.t. each block has constant row sum. It is well known that replacing each block ...