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...

Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under ‘≤’ is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial o...

We prove that there exist only "nitely many nontrivial graphical t-(v; k; ) designs when k 6 4t=3. This improves a previous result of Betten et al. (Discrete Math. 197/198 (1999) 83–109). c © 2001 Elsevier Science B.V. All rights reserved. We use the notation and terminology of [1] and assume that the reader is familiar with the concept of graphical t-designs [2]. All polynomials in this note a...

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...

Kipadia, Nirav Harish. M.S.E.E., Purdue University. May 1994. Pi SIMD Sparse Matrix-Vector Multiplication Algorithm for Computational Electromagnetics and Scattering Matrix Models. Major Professor: Jose Fortes. A large number of problems in numerical analysis require the multiplication of a sparse matrix by a vector. In spite of the large amount of fine-grained parallelism available in the proc...