Mathematical Foundation of Parallel Computing

By: V V Voevodin

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Hardcover | 1 December 1991

At a Glance

Hardcover
364 Pages

Dimensions(cm)
22.23 x 15.88 x 2.54

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Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programs and algorithms into the parallel mode, the choice of appropriate or optimal computer architect and so on. To solve these problems, it is necessary to know very well the structure of algorithms. This book deal with the mathematical mechanism that permits us to investigate structures of both sequential and parallel algorithms. This mechanism allows us to recognize and explain the relations between different methods of constructing parallel algorithms, the methods of analysing round-off errors, the methods of optimizing memory traffic, the methods of working out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.

Industry Reviews

"The book contains a number of exercises helping the reader to master the material ... of interest to researchers in the area of the theory of parallel computing." L S Brim

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Computer Architecture & Logic Design Parallel Processing Mathematics Applied Mathematics Booktopia Publisher Services World Scientific Publishing Discrete Mathematics

Algorithm and Its Graph	p. 1
General notion of algorithm	p. 2
Algorithm notations	p. 6
Graph of algorithm	p. 17
Topological sorting	p. 26
Schedules and graph machine	p. 34
Examples	p. 43
Algorithm Execution Time	p. 55
Vector properties of schedules	p. 57
Number semirings and other sets	p. 67
Minimax properties of schedules	p. 80
Optimal and high-speed schedules	p. 89
Examples	p. 100
Algorithms and Computer Memory	p. 107
Examples	p. 107
Total required memory size	p. 120
Hierarchical memory	p. 135
Sectioning of memory	p. 143
Decomposition of algorithm and of its graph	p. 148
Matrix Investigation of Algorithm Structure	p. 155
Graphs and matrices	p. 156
Recovering the linear functional	p. 164
Computing gradient and derivative	p. 169
Roundoff error analysis	p. 174
Examples	p. 186
Functional Investigation of Algorithm Structure	p. 193
Space-time schedules	p. 193
Regular graphs	p. 203
Passage to the limit	p. 215
Data streams	p. 231
Examples	p. 240
Algorithm Graph and Schedules Building	p. 252
Some statistics	p. 253
Order relation	p. 256
Notation particularities	p. 267
Guidelines for algorithm graph building	p. 275
Splitting the algorithm graph	p. 282
Linear index expressions	p. 292
Branching	p. 301
Linear information closure	p. 308
Examples	p. 313
Afterword	p. 327
References	p. 332
Index	p. 340
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematical Foundation of Parallel Computing

At a Glance

Hardcover

Industry Reviews

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