Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3 n−1, as compared to 2n−1 for the standard partial pivoting. This bound μ...

where Mk,n is the set of all k-by-n matrices with coefficients in {0, 1} and the variables y l are interpreted as follows: y i l = 1 if and only if z i = l. The matrix (y j) can be seen as a {0, 1} assignment matrix where each column contains exactly one coefficient equal to 1 while h denotes the index of the lowest row that is not identically equal to the zero row (cf. Fig. 1). Another variant...

A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The M-matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices A with full column rank for which the generalized inverse A+ & 0. These results are then used to investigate convergent splittings of rectangular matrices...

We consider the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of adjacent ones. We reformulate the problem by using integer programming and we develop approximate solutions based on linearization and convexification techniques.

A two player game (or more correctly, a two player normal-form game) is specified by two m × n payoff matrices R and C corresponding to the row and column player respectively. Each of these matrices has m rows corresponding to the m strategies of the row player and n columns corresponding to the n strategies of the column payer. The row player picks a row i ∈ [m], and the column player picks a ...

A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no...

The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization...

We investigate the balancing of distributed compressed storage of large sparse matrices on a massively parallel computer. For fast computation of matrix{vector and matrix{matrix products on a rectangular processor array with e cient communications along its rows and columns we require that the nonzero elements of each matrix row or column be distributed among the processors located within the s...

In this paper we study the class of m-row matrix compositions (m-compositions, for short), i.e., m-row matrices with nonnegative integer entries in which every column has at least one non-zero element. We provide several enumerative results, various combinatorial identities, and some combinatorial interpretations. Most of these properties are an extension to matrix compositions of the combinato...

The row by row decoupling problem (RRDP) for descriptor systems is considered using proportional state feedback and input transformation. Necessary and sufficient conditions for the solvability of the RRDP are provided. These solvability conditions can be readily verified. A constructive solution to the RRDP is given so that the desired feedback and input transformation matrices can be obtained...