Block memory operations are frequently performed by the operating system and consume an increasing fraction of kernel execution time. These operations include memory copies, page zeroing, interprocess communication, and networking. This thesis demonstrates that performance of these common OS operations is highly dependent on the cache state and future use pattern of the data. This thesis argues...

We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our algorithm requires O(M(n)) elementary operations, whereM(n) is the number of elementary operations needed to multiply n...

The solution of nonsymmetric eigenvalue problems, Ax = λx, can be accelerated substantially by first reducing A to an upper Hessenberg matrix H that has the same eigenvalues as A. This can be done using Householder orthogonal transformations, which is a well established standard, or stabilized elementary transformations. The latter approach, although having half the flops of the former, has bee...

A typical Iranian carbonate matrix block surrounded by an open fracture was modeled in order to understand the fracture-matrix interaction and realize how to model the interaction best. The modeling was carried out by using a fine-scaled Eclipse model in the single porosity mode (the fractures were explicitly modeled). The model was extended to a stack of 6 matrix blocks to understand block-to-...

Using the block vec matrix, I give a necessary and sufficient condition for factorization of a matrix into the Kronecker product of two other matrices. As a consequence, I obtain an elementary algorithmic procedure to decide whether a matrix has a square root for the Kronecker product. Introduction My statistician colleague, J.E. Chacón, asked me how to decide if a real given matrix A has a squ...

This thesis deals with the computation of a small set of exterior eigenvalues of a given large sparse matrix on present (and future) supercomputers using a Block-JacobiDavidson method. The main idea of the method is to operate on blocks of vectors and to combine several sparse matrix-vector multiplications with different vectors in a single computation. Block vector calculations and in particul...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization PAP = LDL where P is a permutation matrix, L is lower triangular with a unit diagonal and D is symmetric block diagonal with 1×1 and 2×2 antidiagonal blocks. The novel algorithm requires O(n2rω−2) arithmetic o...

This paper investigates the performance of block memory operations in the operating system, including memory copies, page zeroing, interprocess communication, and networking. The performance of these common operating system operations is highly dependent on the cache state and future use pattern of the data, and no single routine maximizes performance in all situations. Current systems use a st...

In this paper we consider systolic programs of the most common DSP (convolution, FIR, IIR, FFT) and Matrix (multiplication, triangularisation, linear equation solving, modified Faddeev algorithm) algorithms, executed on systolic arrays of various topologies (linear, 2D mesh, hexagonal). We examine the algorithm-specific parameters (number of I/O paths, unit delays) and program-dependent paramet...