Systolic Computations

By: M.A. Frumkin

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Hardcover | 30 April 1992

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340 Pages

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'Et moi, .. " si j'avait su comment en revenir, je One service mathematics bas rendered the human race. It bas put common sense back n'y serais point aile.' where it belongs, on the topmost shelf next to Jules Verne the dusty canister labelled 'discarded nonsense' . Eric T. Bell The series is divergent; therefore we may be able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'ctre of this series.

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Engineering & Technology Electronics & Communications Engineering Electronics Engineering Circuits & Components Computer Science Computer Architecture & Logic Design Parallel Processing Software Engineering

Mathematics Applied Mathematics Mathematical Modelling Mathematical Theory of Computation Maths for Computer Scientists Databases Data Capture & Analysis

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Published: 28th September 2012

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Series Editor's Preface
Preface
Acknowledgements
VLSI models	p. 1
Short history of the parallel processing	p. 1
Physical opportunities and limits of VLSI	p. 4
Basics of physics of semiconductor devices and integrated circuits	p. 4
Restrictions and opportunities of VLSI technology	p. 9
VLSI model	p. 11
Algorithms for VLSI	p. 16
Representation of algorithms by graphs	p. 16
Representation of computational structures by graphs. The mapping problem	p. 25
The complexity of VLSI computations	p. 29
VLSI complexity and complexity of algorithms	p. 30
Integral measures of VLSI complexity	p. 30
The information content of a function	p. 32
Degree of transitivity of a function	p. 41
Bounded arrays	p. 43
Computations with registers and pebble games	p. 45
Grid model of VLSI design	p. 59
Area-time tradeoff for matrix multiplication	p. 59
Area-time tradeoff for sign detection in the Residue Number System	p. 66
Energy dissipation by computations	p. 70
Complexity of parallel computations	p. 79
Parallel algorithms and complexity	p. 79
NC and RNC classes	p. 81
Parallel algorithms in linear algebra	p. 89
Parallel computations with polynomials and integers	p. 95
Parallel algorithms for combinatorial problems	p. 104
Systolic algorithms and systolic processors	p. 109
Systolic processing	p. 109
Systolic processors for linear algebra	p. 110
Systolic processors for digital signal processing	p. 121
A systolic processor for linear programming problem	p. 143
Systolic processors for mathematical physics	p. 151
Systolic processors for graph problems	p. 155
Mapping systolic algorithms on systolic processors	p. 161
Graphs of systolic processors	p. 169
Meshes	p. 169
Shuffles	p. 172
Trees	p. 180
Embeddings of meshes, trees and shuffles into the hypercube	p. 186
Universal graphs and systolic processors	p. 195
Graph grammars and the generation of graphs	p. 204
Iterations of systolic processors	p. 207
Pipelining and the cut theorem	p. 207
Asynchronous processors	p. 210
Fault tolerance of systolic processors	p. 220
The systolic programming	p. 225
Systolic processors and supercomputers	p. 227
Systolic programming for parallel and vector computers	p. 227
Simulation of SP by the Cray-1 like computer	p. 231
Parallel programming languages	p. 245
Features of parallel programming languages	p. 245
Parallel programming languages	p. 247
Systolic programming in UNIX environment	p. 255
INMOS Transputers	p. 255
Intel i860	p. 259
UNIX system calls for parallel processing	p. 260
Systolic versus parallel programming	p. 265
Appendix 1. Library of systolic algorithms	p. 267
Appendix 2. The grammar of the SPL	p. 272
References	p. 277
Index	p. 313
Table of Contents provided by Blackwell. All Rights Reserved.

Systolic Computations

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Hardcover

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Other Editions and Formats

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