Download or read book An Efficient Algorithm for Sparse Matrix Multiplication written by C. C. Wang and published by . This book was released on 1976 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Efficient Algorithm to Perform Sparse Matrix Multiplication written by F. G. Gustavson and published by . This book was released on 1976 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Efficient Sparse Matrix Multiplication Scheme for the Cyber 205 Computer written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-16 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme. Lambiotte, Jules J., Jr. Langley Research Center NASA-TM-4028, L-16403, NAS 1.15:4028 RTOP 505-90-21-02...

Download or read book Sparse matrix multiplication written by A. Israeli and published by . This book was released on 1984 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Efficient Sparse Matrix Multiplication Scheme for the CYBER 205 Computer written by Jules J. Lambiotte and published by . This book was released on 1988 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Efficient Sparse Matrix Multiplication Scheme for the CYBER 205 Computer written by and published by . This book was released on 1988 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sparse Matrix Technology electronic edition written by Sergio Pissanetzky and published by . This book was released on 1984 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Download or read book Efficient Sparse Matrix Multiplication on a Reconfigurable Mesh written by Hartmut Schmeck and published by . This book was released on 1995 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fast Ultracomputer Algorithm for Sparse Matrix Multiplication written by Amos Israeli and published by . This book was released on 1983 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sparse Matrix Computations written by James R. Bunch and published by Academic Press. This book was released on 2014-05-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

Download or read book Two Fast Algorithms for Sparse Matrices Multiplication and Permuted Transposition written by F. G. Gustavson and published by . This book was released on 1977 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimizing the Performance of Sparse Matrix vector Multiplication written by Eun-Jin Im and published by . This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimizing Sparse Matrix matrix Multiplication for Graph Computations on GPUs and Multi core Systems written by Vineeth Reddy Thumma and published by . This book was released on 2018 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block and a core component for many data analytics and graph algorithms. An efficient parallel SpGEMM implementation has to handle challenges such as irregular nature of the computation and determination of the non-zero entries in the result matrix. In order to overcome these challenges and to exploit the characteristics of the hardware, various algorithms are devised to improve SpGEMM performance on GPUs and multi-core systems. An experimental study is done on Regularized Markov Clustering(R-MCL) algorithm which has SpGEMM as an important primitive and a parallel algorithm has been devised to improve its performance. A new approach to do K-Truss decomposition of a Graph using a variant of SpGEMM has been proposed which uses adjacency matrix formulation.

Download or read book Analysis of High Performance Sparse Matrix vector Multiplication for Small Finite Fields written by Matthew A. Lambert and published by . This book was released on 2020 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis explores the intricacies of obtaining high performance sparse matrix-vector multiplication on modern hardware, with an emphasis on operating over data from small finite fields. We develop and present novel adaptations of classical, fast matrix multiplication algorithms over these fields and apply them in a sparse setting. Further, we compare these novel formats and algorithms to a wide array of standard sparse matrix formats. In particular, we use modern code analysis tools to show how data layouts, vector/panel widths, and choice of compiler all substantially influence the efficiency of the underlying arithmetic of these various sparse formats. These analyses are performed in a data-agnostic manner, meaning we focus solely on the efficiency of the arithmetic and not on higher-level aspects of performance such as cache access patterns. In particular, we analyze the assembly code produced by compilers, removing matrix-specific intangibles from the discussion of format. These are still important considerations when considering any specific matrix, but they make comparing general formats to one another difficult, without exhaustive benchmarking. These results show the theoretical peak arithmetic performance, which we discuss in this abstract, analytic perspective. We see similar trends in synthetic performance benchmarks. Ultimately, we show that the Method of the Four Russians can be directly adapted to sparse matrix-panel (a matrix with relatively few columns) multiplication and that a custom, high-performance variant can achieve high performance in sparse matrix-vector multiplication, with potential to perform better in real-world matrices.

Download or read book Sparse Matrix Technology written by Sergio Pissanetzky and published by Academic Press. This book was released on 2014-06-28 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting.

Download or read book Segmented Operations for Sparse Matrix Computation on Vector Multiprocessors written by Carnegie-Mellon University. Computer Science Dept and published by . This book was released on 1993 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have implemented our algorithm (SEGMV) on the Cray Y-MP C90, and have compared its performance with other methods on a variety of sparse matrices from the Harwell-Boeing collection and industrial application codes. Our performance on the test matrices is up to 3 times faster than the Jagged Diagonal algorithm and up to 5 times faster than Ellpack/Itpack method. Our preprocessing time is an order of magnitude faster than for the Jagged Diagonal algorithm. Also, using an assembly language implementation of SEGMV on a 16 processor C90, the NAS Conjugate Gradient benchmark runs at 3.5 gigaflops."