Several parallel algorithms for Fock matrix construction are described. The algorithms calculate only the unique integrals, distribute the Fock and density matrices over the processors of a massively parallel computer, use blocking techniques to construct the distributed data structures, and use clustering techniques on each processor to maximize data reuse. Algorithms based on both square and ...

The efficiency of the one-sided parallel block-Jacobi algorithm for computation of the singular value decomposition (SVD) of a general matrix A ∈ Rm×n, m ≥ n, depends–besides some numerical tricks that speed-up the convergence–crucially on the parallel ordering of subproblems, which are to be solved in each parallel iteration step. We discuss in detail possible generalizations of the so-called ...

Nunierically stable and computationally efficient Power System Statc Estimation (PSSE) algorithms are designed using Orthogonalization (QR decomposition) approach. They u3e Givens rotations for orthogonalization which enables sparsity exploitation during factorization of large sparse auginentecl Ja,cobian. Apriori row and column ordering is usiially performed to reduce intermediate a.nd and ove...

The solution of chemical process simulation and optimization problems on today's high performance supercomputers requires algorithms that can take advantage of vector and parallel processing when solving the large, sparse matrices that arise. The frontal method can be highly e cient in this context due to its ability to make use of vectorizable dense matrix kernels on a relatively small frontal...

Complete row and column symmetry breaking in constraint satisfaction problems using the lex leader method is generally prohibitively costly. Double lex, which is derived from lex leader, is commonly used in practice as an incomplete symmetry-breaking method for row and column symmetries. This technique uses a row-wise ordering to construct the lex leader. For this reason, it is generally counte...

In a constraint satisfaction problem (CSP), symmetry involves the variables, values in the domains, or both, and maps each search state into an equivalent one. When searching for solutions, symmetrically equivalent (partial) assignments can dramatically increase the search space. Hence, elimination of symmetry is essential to avoid exploring equivalent branches in a search tree. An important cl...

This paper analyzes the performance and scalability of an iteration of the Preconditioned Conjugate Gradient Algorithm on parallel architectures with a variety of interconnection networks, such as the mesh, the hypercube, and that of the CM-5T M † parallel computer. It is shown that for block-tridiagonal matrices resulting from two dimensional finite difference grids, the communication overhead...

The successive over-relaxation (SOR) how to quickly verify and generate a iterative method is an important solver for linear multicoloring ordering according to the given systems. In this paper, a parallel algorithm for the structure of a matrix or a grid. However, the red-black SOR method with domain decomposition is multi-color SOR method is parallel only within investigated. The parallel SOR...

One of the graph theoretic approaches of channel assignment for cellular networks is routing a pair of nodes arranged in a single-row axis called single-row routing problem. The network with nodes representing caller and receiver is to be transformed into a single-row network efficiently is proposed. The connected graph derived from the base network is presented using incidence matrix. The rows...