Parallel Algorithms for Matrix Computations

Parallel Algorithms for Matrix Computations

Author: K. Gallivan

Publisher: SIAM

Published: 1990-01-01

Total Pages: 207

ISBN-13: 9781611971705

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Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.


Singapore Supercomputing Conference '90: Supercomputing For Strategic Advantage

Singapore Supercomputing Conference '90: Supercomputing For Strategic Advantage

Author: Kang Hoh Phua

Publisher: World Scientific

Published: 1991-09-10

Total Pages: 496

ISBN-13: 9814555991

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Supercomputing is a strategic tool for the future. These proceedings examine the most recent advances in effective applications of supercomputing and offer provocative visions of the future. Special focus is given to the spread of applications in both the public and commercial sectors where supercomputing is being increasingly embraced as the ultimate competitive tool in the global arena.


Task Scheduling for Parallel Systems

Task Scheduling for Parallel Systems

Author: Oliver Sinnen

Publisher: John Wiley & Sons

Published: 2007-05-04

Total Pages: 326

ISBN-13: 0471735760

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A new model for task scheduling that dramatically improves the efficiency of parallel systems Task scheduling for parallel systems can become a quagmire of heuristics, models, and methods that have been developed over the past decades. The author of this innovative text cuts through the confusion and complexity by presenting a consistent and comprehensive theoretical framework along with realistic parallel system models. These new models, based on an investigation of the concepts and principles underlying task scheduling, take into account heterogeneity, contention for communication resources, and the involvement of the processor in communications. For readers who may be new to task scheduling, the first chapters are essential. They serve as an excellent introduction to programming parallel systems, and they place task scheduling within the context of the program parallelization process. The author then reviews the basics of graph theory, discussing the major graph models used to represent parallel programs. Next, the author introduces his task scheduling framework. He carefully explains the theoretical background of this framework and provides several examples to enable readers to fully understand how it greatly simplifies and, at the same time, enhances the ability to schedule. The second half of the text examines both basic and advanced scheduling techniques, offering readers a thorough understanding of the principles underlying scheduling algorithms. The final two chapters address communication contention in scheduling and processor involvement in communications. Each chapter features exercises that help readers put their new skills into practice. An extensive bibliography leads to additional information for further research. Finally, the use of figures and examples helps readers better visualize and understand complex concepts and processes. Researchers and students in distributed and parallel computer systems will find that this text dramatically improves their ability to schedule tasks accurately and efficiently.


Compiling Parallel Loops for High Performance Computers

Compiling Parallel Loops for High Performance Computers

Author: David E. Hudak

Publisher: Springer Science & Business Media

Published: 1992-10-31

Total Pages: 180

ISBN-13: 0792392833

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4. 2 Code Segments . . . . . . . . . . . . . . . 96 4. 3 Determining Communication Parameters . 99 4. 4 Multicast Communication Overhead · 103 4. 5 Partitioning . . . . . . · 103 4. 6 Experimental Results . 117 4. 7 Conclusion. . . . . . . · 121 5 COLLECTIVE PARTITIONING AND REMAPPING FOR MULTIPLE LOOP NESTS 125 5. 1 Introduction. . . . . . . . . 125 5. 2 Program Enclosure Trees. . 128 5. 3 The CPR Algorithm . . 132 5. 4 Experimental Results. . 141 5. 5 Conclusion. . 146 BIBLIOGRAPHY. 149 INDEX . . . . . . . . 157 LIST OF FIGURES Figure 1. 1 The Butterfly Architecture. . . . . . . . . . 5 1. 2 Example of an iterative data-parallel loop . . 7 1. 3 Contiguous tiling and assignment of an iteration space. 13 2. 1 Communication along a line segment. . . 24 2. 2 Access pattern for the access offset, (3,2). 25 2. 3 Decomposing an access vector along an orthogonal basis set of vectors. . . . . . . . . . . . . . . . . . . 26 2. 4 An analysis of communication patterns. 29 2. 5 Decomposing a vector along two separate basis sets of vectors. 31 2. 6 Cache lines aligning with borders. 33 2. 7 Cache lines not aligned with borders. 34 2. 8 nh is the difference of nd and nb. 42 2. 9 nh is the sum of nd and nb. 42 2. 10 The ADAPT system. 44 2. 11 Code segment used in experiments. . 46 2. 12 Execution rates for various partitions. 47 2. 13 Execution time of partitions on Multimax. 48 2. 14 Performance increase as processing power increases. 49 2. 15 Percentage miss ratios for various aspect ratios and line sizes.


Parallel Processing from Applications to Systems

Parallel Processing from Applications to Systems

Author: Dan I. Moldovan

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 586

ISBN-13: 1483297519

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This text provides one of the broadest presentations of parallel processing available, including the structure of parallelprocessors and parallel algorithms. The emphasis is on mapping algorithms to highly parallel computers, with extensive coverage of array and multiprocessor architectures. Early chapters provide insightful coverage on the analysis of parallel algorithms and program transformations, effectively integrating a variety of material previously scattered throughout the literature. Theory and practice are well balanced across diverse topics in this concise presentation. For exceptional clarity and comprehension, the author presents complex material in geometric graphs as well as algebraic notation. Each chapter includes well-chosen examples, tables summarizing related key concepts and definitions, and a broad range of worked exercises. - Overview of common hardware and theoretical models, including algorithm characteristics and impediments to fast performance - Analysis of data dependencies and inherent parallelism through program examples, building from simple to complex - Graphic and explanatory coverage of program transformations - Easy-to-follow presentation of parallel processor structures and interconnection networks, including parallelizing and restructuring compilers - Parallel synchronization methods and types of parallel operating systems - Detailed descriptions of hypercube systems - Specialized chapters on dataflow and on AI architectures