We present two implementations of dense matrix multiplication based on two different non-canonical array layouts: one based on a hypermatrix data structure (HM) where data submatrices are stored using a recursive layout; the other based on a simple block data layout with square blocks (SB) where blocks are arranged in column-major order. We show that the iterative code using SB outperforms a re...

The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour. Two decades later Lars Onsager solved the Ising problem for the quadratic ...

This paper presents a new algorithm for computing the Hermite normal form H of an A 2 Z Z nm of rank m together with a unimodular pre-multiplier matrix U such that UA = H. Our algorithm requires O~(m ?1 nM(m log jjAjj)) bit operations to produce both H and a candidate for U. Here, jjAjj = maxij jAijj, M(t) bit operations are suucient to multiply two dte-bit integers, and is the exponent for mat...

Abstract argumentation frameworks with finitely many arguments can be presented in matrix form. For this reason, the strengths and weaknesses of matrix operations are migrated from a mathematical representation to a computer science interpretation. We present matrix operation algorithms that can answer whether a given set of arguments is part of an argumentation extension.argumentation framewor...

In the analysis of spatial data, the inverse of the covariance matrix needs to be calculated. For example, the inverse is needed for best linear unbiased prediction or kriging, and is repeatedly calculated in the maximum likelihood estimation or the Bayesian inferences. Since the spatial sample size can be quite large, operations on the large covariance matrix can be a numerical challenge if no...

In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subd...

In this paper, we present two algorithms for sparse banded matrix-vector and sparse banded matrix-matrix product operations on distributed memory multiprocessor systems that support a mesh and ring interconnection topology. We aslo study the scalability of these two algorithms. We employ systolic type techniques to eliminate synchronization delay and minimize the communication overhead among pr...

A general scheme is proposed for computing the QR-factorization of certain displacement structured matrices, including Cauchy-like, Vandermonde-like, Toeplitz-like and Hankel-like matrices, hereby extending some earlier work for the QR-factorization of the Cauchy matrix. The algorithm employs a chasing scheme for the recursive construction of a diagonal plus semiseparable matrix of semiseparabi...

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

We compute the Newton step for the characteristic polynomial and for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix as the reciprocal of the trace of an appropriate matrix. We show that, after the Yule–Walker equations are solved, this trace can be computed in O(n) additional arithmetic operations, which is in contrast to existing methods, which rel...