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...

We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum.

Utilizing the concept of Perron complement, a new estimate for the spectral radius of a nonnegative irreducible matrix is presented. A new matrix is derived that preserves the spectral radius while its minimum row sum increases and its maximum row sum decreases. Numerical examples are provided to illustrate the effectiveness of this approach.

This paper shows that nding the row minima (maxima) in an nn totally monotone matrix in the worst case requires any algorithm to make 3n ? 5 comparisons or 4n ? 5 matrix accesses. Where the, so called, SMAWK algorithm of Aggarwal et al. nds the row minima in no more than 5n ? 2 lg n ? 6 comparisons.

Utilizing the concept of Perron complement, a new estimate for the spectral radius of a nonnegative irreducible matrix is presented. A new matrix is derived that preserves the spectral radius while its minimum row sum increases and its maximum row sum decreases. Numerical examples are provided to illustrate the effectiveness of this approach.

Nonnegative Matrix Factorization (NMF) is more and more frequently used for analyzing large-scale nonnegative data, where the number of samples and/or the number of observed variables is large. In the paper, we discuss two applications of the row-action projections in the context of learning latent factors from large-scale data. First, we show that they can be efficiently used for improving the...

There are characteristics of Hadamard matrices that enable an exhaustive search using algorithmic techniques. The search derives primarily from the eigenvalues which are constant after the Hadamard matrix is multiplied by its transpose. Generally this would be a performance concern but there are additional properties that enable the eigenvalues to be predicted. Here an algorithm is given to obt...

We present an algorithmic analog-to-digital converter (ADC) architecture for large-scale parallel quantization of internally analog variables in externally digital array processors. The converter quantizes and accumulates a binary weighted sequence of partial binary-binary matrix-vector products computed on the analog array, under presentation of bit-serial inputs in descending binary order. Th...