Partitioning Of Matrices Research Articles

Graph coloring, minimum-diameter partitioning, and the analysis of confusion matrices

It is well known that minimum-diameter partitioning of symmetric dissimilarity matrices can be framed within the context of coloring the vertices of a graph. Although confusion data are typically represented in the form of asymmetric similarity matrices, they are also amenable to a graph-coloring perspective. In this paper, we propose the integration of the minimum-diameter partitioning method with a neighborhood-based coloring approach for analyzing digraphs corresponding to confusion data. This procedure is capable of producing minimum-diameter partitions with the added desirable property that vertices with the same color have similar in-neighborhoods (i.e., directed edges entering the vertex) and out-neighborhoods (i.e., directed edges exiting the vertex) for the digraph corresponding to the minimum partition diameter.

Partitioned sparse A/sup -1/ methods (power systems)

The classic Ax=b problem in the partitioning of sparse vector matrices is solved by constructing factored components of the inverses of L and U, the triangular factors of matrix A. The number of additional fill-ins in the partitioned inverses of L and U can be made zero. The number of partitions is related to the path length of sparse vector methods. Allowing some fill-in in the partitioned inverses of L and U results in fewer partitions. Ordering algorithms most suitable for sparsity preservation in the inverses of L and U require addition fill-in in L and U themselves. Tests on practical power system matrices with from 118 to 1993 nodes indicate that the proposed approach is competitive in serial environments, and appears more suitable for parallel environments. Because sparse vectors are not required, the approach works not only for short-circuit calculations but also for power flow and stability computations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Partitioning and preconditioning of finite element matrices on the DAP

A method for solving linear finite element equations is proposed for highly parallel SIMD architectures with limited local memory. The method is based on a fine domain decomposition that can be conveniently mapped onto the processor array. Then the equations are structured using a form of one-way dissection and the equations solved by an iteration that combines conjugate gradient relaxation with coarse grid smoothing. Numerical experiments using the 64 × 64 DAP are presented.

Decentralized control using quasi-block diagonal dominance of transfer function matrices

The purpose of this paper is to present a generalization of the Nyquist array method to blockwise decompositions, which is based upon a new version of block diagonal dominance. An additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices, which increases considerably the class of control systems which can be designed via block diagonal dominance. Within this framework, the controllers for individual subsystems can be designed independently of each other, so that their union represents a decentralized controller for the overall system.

Block-successive approximation for a discounted Markov decision model

In this paper we suggest a new successive approximation method to compute the optimal discounted reward for finite state and action, discrete time, discounted Markov decision chains. The method is based on a block partitioning of the (stochastic) matrices corresponding to the stationary policies. The method is particularly attractive when the transition matrices are jointly nearly decomposable or nearly completely decomposable.

The Partitioning of Matrices in Structural Analysis

Abstract The practical value of the partitioning of matrices in structural analysis is illustrated with the solution of two multicell box beams in torsion. The desirability of partitioning a matrix is determined from a simple principle relating to the pattern of the matrix. Typical patterns of matrices that are readily inverted are noted and employed in the solution by matrix partitioning.