Matrix interpretations can be used to bound the derivational complexity of rewrite systems. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. It includes the method of upper triangular interpretations as a special case, and we prove that the inclusion is strict. The criterion can be expressed as a finite domain constraint system. It trans...

We propose a divide-and-conquer algorithm for computing arbitrary functions of upper triangular matrices, which requires approximately the same number of arithmetic operations as Parlett’s algorithm. However, the new algorithm has better performance on computers with two levels of memory due to its block structure and thus, less memory-cache traffic requirements. Like Parlett’s algorithm, the n...

1.1 The number.dat data file from Shepard, Kilpatric, and Cunningham (1975). 11 3.1 A proximity matrix, morse digits.dat, for the 10 Morse code symbols representing the first ten digits 9.1 Order-constrained least-squares approximations to the digit proximity data of Shepard et al. (1975); the upper-triangular portion is anti-Robinson and the lower-triangular portion is strongly-anti-9.2 The 45...

Associating to each pre-order on the indices 1; :::;n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n n matrix rings. Rings within the order-convex hull of the embedding, i.e. matrix rings that contain the ring of diagonal matrices, can be viewed as incidence algebras of ideal-valued, generalized pre-order relation...

We use the matrix-geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady-state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981),...

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues.

We prove a lower bound of 52n2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

In the forward phase, GreedyInverseCovariance() selects the top bs candidates by calling ForwardEvaluator() (Algorithm 1). Briefly, this algorithm checks each of the (as yet unselected) positions in the upper (or lower) triangular matrix of W and returns a map of the top bs candidates. For each candidate, αij is computed and subsequently, the likelihood when αij(eij + eji) is added to W is comp...

An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.