The matrix chain ordering problem is to find the cheapest way to multiply a chain of n matrices, where the matrices are pairwise compatible but of varying dimensions. Here we give several new parallel algorithms including O(lg3 n)-time and n/lgn-processor algorithms for solving the matrix chain ordering problem and for solving an optimal triangulation problem of convex polygons on the common CR...

In order to efficiently compute some combinatorial designs based upon circulant matrices which have different, defined numbers of 1's and 0's in each row and column we need to find candidate vectors with differing weights and Hamming distances. This paper concentrates on how to efficiently create such circulant matrices. These circulant matrices have applications in signal processing, public ke...

Two opposing patterns of meta-community organization are nestedness and negative species co-occurrence. Both patterns can be quantified with metrics that are applied to presence-absence matrices and tested with null model analysis. Previous meta-analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co-...

Consider an invertible n × n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n row operations and in general that many operations might be needed. In [1] the authors considered matrices in GL(n, q), the set of n × n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which perfor...

In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling.

Let Sn(S) denote the set of symmetric matrices over some semiring, S. A line of A ∈ Sn(S) is a row or a column of A. A star of A is the submatrix of A consisting of a row and the corresponding column of A. The term rank of A is the minimum number of lines that contain all the nonzero entries of A. The star cover number is the minimum number of stars that contain all the nonzero entries of A. Th...

with Application to Gene-Expression Analysis Sepp Hochreiter [email protected] Klaus Obermayer Fakultät für Elektrotechnik und Informatik Technische Universität Berlin Franklinstr. 28/29, 10587 Berlin, Germany [email protected] We consider the classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects where row and column ...

Some large rectangular matrices used in animal breeding are presented. We describe how to generate these matrices from the data supplied by animal breeders. The matrices are very sparse (3 nonzeros per row) and range between 26 20 and 968 652 582 694.

A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper...