In many large scale scientiic and engineering computations, the solution to a sparse linear system is required. We present a partial unsymmetric nested dissection method that can be used to parallelize any general unsymmetric sparse matrix algorithm whose pivot search can be restricted to a subset of rows and columns in the active submatrix. The submatrix is determined by the partial unsymmetri...

The Moore-Penrose inverse of a real matrix having no square submatrix with two or more diagonals is described in terms of bipartite graphs. For such a matrix, the sign of every entry of the Moore-Penrose inverse is shown to be determined uniquely by the signs of the matrix entries; i.e., the matrix has a signed generalized inverse. Necessary and sufficient conditions on an acyclic bipartite gra...

In this paper, based on the assumption that both the leading principal submatrix of r-order and its complementary submatrix in A(t) have eigenvalues with only negative real parts, we establish a criterion for the stability of a class of nonlinear time-varying dynamic system dx/dt = A(t)x+ f(t, x). Also a feasible method for decomposition and aggregation of large-scale system is provided. Moreov...

We define the determinantal divisor rank of an integral matrix to be the number of invariant factors which equal 1. Some properties of the determinantal divisor rank are proved, which are analogous to known properties of the usual rank. These include the Frobenious inequality for the rank of a product and a relation between the rank of a submatrix of a matrix and that of its complementary subma...

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the p...

For a given matrix of size n ×m over a finite alphabet A, a bicluster is a submatrix composed of selected columns and rows satisfying a certain property. In microarrays analysis one searches for largest biclusters in which selected rows constitute the same string (pattern); in another formulation of the problem one tries to find a maximally dense submatrix. In a conceptually similar problem, na...

Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer ≤ n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of M of order k. The proof uses results about random walks on symmetric groups and concentration of measure. In a similar way, we also show that almost all k × n submatrices of M h...