Representation of belief states is an important issue for knowledge based systems. In this paper, we develop a matrix representation for ordered belief states and show that belief reasoning, revision and fusion can all be interpreted as operations of matrix algebra. Thus, the matrix representation can serve as the basis of algebraic semantics for belief logic.

Second order algorithms are very efficient for neural network training because of their fast convergence. In traditional Implementations of second order algorithms [Hagan and Menhaj 1994], Jacobian matrix is calculated and stored, which may cause memory limitation problems when training large-sized patterns. In this paper, the proposed computation is introduced to solve the memory limitation pr...

The usual QR algorithm for finding the eigenvalues of a Hessenberg matrix H is based on vector-vector operations, e.g. adding a multiple of one row to another. The opportunities for parallelism in such an algorithm are limited. In this report, we describe a reorganization of the QR algorithm to permit either matrix-vector or matrix-matrix operations to be performed, both of which yield more eff...

Stoicheiometric analysis of metabolic pathways provides a systematic way of determining which metabolite concentrations are subject to constraints, information that may otherwise be very difficult to recognize in a large branched pathway. The procedure involves representing the pathway structure in the form of a matrix and then carrying out row operations to convert the matrix into "row echelon...

(1) A system of linear equations can be stored using an augmented matrix. The part of the matrix that does not involve the constant terms is termed the coefficient matrix. (2) Variables correspond to columns and equations correspond to rows in the coefficient matrix. The augmented matrix has an extra column corresponding to the constant terms. (3) In the paradigm where the system of linear equa...

Address computations and indirect, hence double, memory accesses in sparse matrix application software render sparse computations to be ine cient in general. In this paper we propose memory architectures that support the storage of sparse vectors and matrices. In a rst design, called vector storage, a matrix is handled as an array of sparse vectors, stored as singly-linked lists. Deletion and i...

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM implementation has to handle extra irregularity from three aspects: (1) the number of nonzero entries in the resulting sparse m...

Sparse matrix-vector multiplication is an important computational kernel that tends to perform poorly on modern processors, largely because of its high ratio of memory operations to arithmetic operations. Optimizing this algorithm is difficult, both because of the complexity of memory systems and because the performance is highly dependent on the nonzero structure of the matrix. The Sparsity sy...

Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial diierential equations. The large size and the condition of many technical or physical applications in this area result in the need for eecient par-allelization and preconditioning techniques of the CG method. In particular for very ill-condition...

We investigate the expressive power of MATLANG, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation inv of inverting a matrix. In MATLANG + inv we can compute the transitive closure of directed graphs, whereas we show that this is not possible without inversion. Indeed we show that the basic language can...