7 research outputs found

    Engineering Physics and Mathematics Division progress report for period ending December 31, 1994

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    Design and analysis of numerical algorithms for the solution of linear systems on parallel and distributed architectures

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    The increasing availability of parallel computers is having a very significant impact on all aspects of scientific computation, including algorithm research and software development in numerical linear algebra. In particular, the solution of linear systems, which lies at the heart of most calculations in scientific computing is an important computation found in many engineering and scientific applications. In this thesis, well-known parallel algorithms for the solution of linear systems are compared with implicit parallel algorithms or the Quadrant Interlocking (QI) class of algorithms to solve linear systems. These implicit algorithms are (2x2) block algorithms expressed in explicit point form notation. [Continues.

    Efficient Utilization of Fine-Grained Parallelism using a microHeterogeneous Environment

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    The goal of this thesis is to propose a new computing paradigm, called micro- Heterogeneous computing or mHC, which incorporates PCI (or other high speed local system bus) based processing elements (vector processors, digital signal processors, etc) into a general purpose machine. In this manner the benefits of heterogeneous computing on scientific applications can be achieved while avoiding some of the lim itations. Overall performance is increased by exploiting fine-grained parallelism on the most efficient architecture available, while reducing the high communication over head and costs of traditional heterogeneous environments. Furthermore, mHC based machines can be combined into a cluster, allowing both the coarse-grained and fine grained parallelism to be fully exploited in order to achieve even greater levels of performance. An existing high performance computing API (GSL) was chosen as the interface to the system to allow for easy integration with applications that were previously developed using this API. The ensuing chapters will provide the motivation for this work, an overview of heterogenous computing, and the details pertaining to microHeterogeneous comput ing. The framework implemented to demonstrate a microHeterogeneous computing environment will be examined as well as the results. Finally, the future of micro Heterogeneous computing will be discussed

    Hybrid algorithms for efficient Cholesky decomposition and matrix inverse using multicore CPUs with GPU accelerators

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    The use of linear algebra routines is fundamental to many areas of computational science, yet their implementation in software still forms the main computational bottleneck in many widely used algorithms. In machine learning and computational statistics, for example, the use of Gaussian distributions is ubiquitous, and routines for calculating the Cholesky decomposition, matrix inverse and matrix determinant must often be called many thousands of times for common algorithms, such as Markov chain Monte Carlo. These linear algebra routines consume most of the total computational time of a wide range of statistical methods, and any improvements in this area will therefore greatly increase the overall efficiency of algorithms used in many scientific application areas. The importance of linear algebra algorithms is clear from the substantial effort that has been invested over the last 25 years in producing low-level software libraries such as LAPACK, which generally optimise these linear algebra routines by breaking up a large problem into smaller problems that may be computed independently. The performance of such libraries is however strongly dependent on the specific hardware available. LAPACK was originally developed for single core processors with a memory hierarchy, whereas modern day computers often consist of mixed architectures, with large numbers of parallel cores and graphics processing units (GPU) being used alongside traditional CPUs. The challenge lies in making optimal use of these different types of computing units, which generally have very different processor speeds and types of memory. In this thesis we develop novel low-level algorithms that may be generally employed in blocked linear algebra routines, which automatically optimise themselves to take full advantage of the variety of heterogeneous architectures that may be available. We present a comparison of our methods with MAGMA, the state of the art open source implementation of LAPACK designed specifically for hybrid architectures, and demonstrate up to 400% increase in speed that may be obtained using our novel algorithms, specifically when running commonly used Cholesky matrix decomposition, matrix inverse and matrix determinant routines

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
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