Introduction to Parallel and Vector Solution of Linear Systems (Google eBook)

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Springer Science & Business Media, Apr 30, 1988 - Computers - 305 pages
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Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
  

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Contents

Introduction
1
12 Basic Concepts of Parallelism and Vectorization
20
13 Matrix Multiplication
36
Direct Methods for Linear Equations
59
22 Direct Methods Tor Parallel Computers
85
23 Banded Systems
108
Iterative Methods for Linear Equations
133
32 The GaussSeidel and SOR Iterations
156
34 The Preconditioned Conjugate Gradient Method
196
The ijk Forms of LU and Choleski Decomposition
235
Convergence of Iterative Methods
253
The Conjugate Gradient Algorithm
269
Basic Linear Algebra
281
Bibliography
285
Index
299
Copyright

33 Minimization Methods
185

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