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Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph. This is the situation of the domination number, the Roman domination number or the 2-domination number, among others. Contrary to what happens with the domination number and the Roman domination number, the 2-domination number remains unknown in cylinders, that is, the Cartesian product of a cycle and a path and in this paper, we will compute this parameter in the cylinders with small cycles. We will develop two algorithms involving the (min, +) matrix product that will allow us to compute the desired values of γ2(Cn□Pm), with 3 ≤ n ≤ 15 and m ≤ 2. We will also pose a conjecture about the general formula for the 2-domination number in this graph class. [ABSTRACT FROM AUTHOR]

The resolution of the 3D Helmholtz equation is required in the development of models related to a wide range of scientific and technological applications. For solving this equation in complex arithmetic, the biconjugate gradient (BCG) method is one of the most relevant solvers. However, this iterative method has a high computational cost because of the large sparse matrix and the vector operations involved. In this paper, a specific BCG method, adapted for the regularities of the Helmholtz equation is presented. This BCG is based on the implementation of a novel format (named 'Regular Format') that allows the storage of the large sparse matrix involved in the sparse matrix vector product in a compact form. The contribution of this work is twofold: (1) decreasing the memory requirements of the 3D Helmholtz equation using the 'Regular Format' and (2) speeding up the resolution of the equation using high performance computing resources. A hybrid Message Passing Interface (MPI)-graphics processing unit CUDA GPU parallelization that is capable of solving complex problems in short time has carried out (Fast-Helmholtz). Fast-Helmholtz combines optimizations at Message Passing Interface and GPU levels to reduce communications costs and to improve the exploitation of GPU architecture. This strategy makes it possible to extend the dimension of the Helmholtz problem to be solved, thanks to the relevant reduction of memory requirements and runtime. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Sparse matrix matrix (SpMM) multiplication is involved in a wide range of scientific and technical applications. The computational requirements for this kind of operation are enormous, especially for large matrices. This paper analyzes and evaluates a method to efficiently compute the SpMM product in a computing environment that includes graphics processing units (GPUs). Some libraries to compute this matricial operation can be found in the literature. However, our strategy (FastSpMM) outperforms the existing approaches because it combines the use of the ELLPACK-R storage format with the exploitation of the high ratio computation/memory access of the SpMM operation and the overlapping of CPU–GPU communications/computations by Compute Unified Device Architecture streaming computation. In this work, FastSpMM is described and its performance evaluated with regard to the CUSPARSE library (supplied by NVIDIA), which also includes routines to compute SpMM on GPUs. Experimental evaluations based on a representative set of test matrices show that, in terms of performance, FastSpMM outperforms the CUSPARSE routine as well as the implementation of the SpMM as a set of sparse matrix vector products. [ABSTRACT FROM AUTHOR]

Electron tomography (ET) is an important technique in biosciences that is providing new insights into the cellular ultrastructure. Iterative reconstruction methods have been shown to be robust against the noise and limited-tilt range conditions present in ET. Nevertheless, these methods are not extensively used due to their computational demands. Instead, the simpler method weighted backprojection (WBP) remains prevalent. Recently, we have demonstrated that a matrix approach to WBP allows a significant reduction in processing time both on central processing units and on graphics processing units (GPUs). In this work, we extend that matrix approach to one of the most common iterative methods in ET, simultaneous iterative reconstruction technique (SIRT). We show that it is possible to implement this method targeted at GPU directly, using sparse algebra. We also analyse this approach on different GPU platforms and confirm that these implementations exhibit high performance. This may thus help to the widespread use of SIRT. [ABSTRACT FROM AUTHOR]

This paper presents an initiative to teach computer representation of numbers and arithmetic in undergraduate courses in computer science and engineering. The approach is based upon carefully designed practical exercises that highlight the main properties and computational issues of finite-length number representation and arithmetic. In conjunction with the exercises, an auxiliary computer-based environment constitutes a valuable support tool for students to learn and understand the concepts involved. For integer representation, this work has focused on the standard 2's complement. Special emphasis has been put on the algorithms for integer arithmetic operations. For floating-point representation, simpler formats have been used as an introduction to the IEEE Standard 754, with the aim of presenting the fundamentals of the floating-point computation and emphasizing its limitations. This approach could be included in introductory courses related to computer organization, programming, discrete mathematics, or numerical methods. [ABSTRACT FROM AUTHOR]

Optical Diffraction Tomography has been recently introduced in fluid velocimetry to provide three dimensional information of seeding particle locations. In general, image reconstruction methods at visible wavelengths have to account for diffraction. Linear approximation has been used for three-dimensional image reconstruction, but a non-linear and iterative reconstruction method is required when multiple scattering is not negligible. Non-linear methods require the solution of the Helmholtz equation, computationally highly demanding due to the size of the problem. The present work shows the results of a non-linear method customized for spherical particle location using GPU computing and a made-to-measure storing format.