8 Elementary operations and the rank of a matrix 25 8.1 Gauss transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 8.2 Elementary row operations . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.3 The augmented matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.4 Row reducing a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8.5 Elem...

Let (I be a column of the fft x /I matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy IO see that if Y,~,(A) denotes . the columns implied by A, than :/,,,(A) is a closure operation. We say that M represents this closure operation. s(:/ ) is the minimum number of the rows of the matrices representing a given closure ...

This paper compares various contemporary multi-core based microprocessor architectures with different memory interconnects regarding performance, speedup, and parallel efficiency. Sparse matrix operations are used as a benchmark application from the area of electrical engineering. Within this context, thread to core pinnning and cache optimization are two important aspects which are investigate...

This thesis discusses the matrix container template I implemented as part of the STXXL library for very large data sets. Because it is designed for matrices too big to be held in internal memory, algorithms and data structures are chosen to be efficient for external memory operation. Transposition, addition, and scalar multiplication are easy; therefore their description is kept brief. Matrix m...

Our approach is to chop matrixes into an array of square tiles of uniform size and use DryadLINQ to construct and execute a distributed execution plan for passing tiles between compute nodes from stage to stage of the computation of a large matrix operation. We use HPC Dryad Beta [5] running on an 85-node cluster for distributed execution and BLAS routines from the Intel R © Math Kernel Libary ...

We consider Padberg’s conjecture about almost totally unimodular matrices proposed in 1988 in Operations Research Letters. We show that it is not correct as stated and give a modi ed version of the conjecture. c © 2000 Published by Elsevier Science B.V. All rights reserved.

Here we investigate how the spectrum of the normalized graph Laplacian gets affected by certain graph operations like motif duplication and graph (or motif) joining.

The output of modern imaging techniques such as diffusion tensor MRI or the physical measurement of anisotropic behaviour in materials such as the stress-tensor consists of tensor-valued data. Hence adequate image processing methods for shape analysis, skeletonisation, denoising and segmentation are in demand. The goal of this paper is to extend the morphological operations of dilation, erosion...

Efficiently manipulating and operating on block matrices can be beneficial in many applications, among others those involving iteratively solving nonlinear systems. These types of problems consist of repeatedly assembling and solving sparse linear systems. In the case of very large systems, without a careful manipulation of the corresponding matrices, solving can become very time consuming. Thi...

Algorithms are called cache oblivious, if they are designed to benefit from any kind of cache hierarchy—regardless of its size or number of cache levels. In linear algebra computations, block recursive approaches are a common approach that, by construction, lead to inherently local data access pattern, and thus to an overall good cache performance[3]. In this article, we present block recursive...