Download PDF by Ronald W. Shonkwiler: An Introduction to Parallel and Vector Scientific Computing

By Ronald W. Shonkwiler

ISBN-10: 0521683378

ISBN-13: 9780521683371

ISBN-10: 052186478X

ISBN-13: 9780521864787

During this textual content, scholars of utilized arithmetic, technology and engineering are brought to basic methods of puzzling over the wide context of parallelism. The authors start by way of giving the reader a deeper realizing of the problems via a basic exam of timing, information dependencies, and conversation. those rules are applied with recognize to shared reminiscence, parallel and vector processing, and dispensed reminiscence cluster computing. Threads, OpenMP, and MPI are coated, besides code examples in Fortran, C, and Java. the foundations of parallel computation are utilized all through because the authors hide conventional issues in a primary direction in medical computing. development at the basics of floating aspect illustration and numerical blunders, an intensive remedy of numerical linear algebra and eigenvector/eigenvalue difficulties is equipped. via learning how those algorithms parallelize, the reader is ready to discover parallelism inherent in different computations, resembling Monte Carlo tools.

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Extra resources for An Introduction to Parallel and Vector Scientific Computing

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S11 s12 s13 s14 s25 .. s2r −3,2r . P1: FCW CUNY470-Shonkwiler 36 0 521 86478 X May 15, 2006 7:54 2 Theoretical Considerations – Complexity If n is not a power of 2, as above we proceed as if the complement to the next power of 2 is filled out with 0s. This adds 1 to the time. We have the following results. Using 1 processor, T1 = n − 1 and, using p = n − 1 processors, T∞ = Tn−1 = r = log n . The speedup is SU (n − 1) = n−1 , and the efficiency is E f = log1 n . So the efficiency is better but still log n as n → ∞, E f → 0.

7:21 25 of one half the terms. ) Find the time required and MFLOPs for this pseudo-vectorization. (b) Suppose the vector startup must be paid only once, since after that, the arguments are in the vector registers. Now what is the time? (c) Using your answer to part (b), time the inner product of 2n length vectors, and compare with the Vector Timing Data Table (p. 11). (3) Given the data of Table 1 for a vector operation and a saxpy operation, find s and l. (6) Show how to do an n × n matrix vector multiply y = Ax on a ring, a 2-dimensional mesh and a hypercube, each of appropriate size.

Hence it is important to be explicit about its meaning. After speedup, another important consideration is the fraction of time the processors assigned to a computation are kept busy. This is called the efficiency of the parallelization using p processors and is defined by E f ( p) = SU ( p) . 2 Some Basic Complexity Calculations 33 Fig. 13. DAG for vector addition. Fig. 14. DAG for reduction. Efficiency measures the average time the p processors are working. If the speedup is linear meaning equal to p, then the efficiency will be 100%.

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An Introduction to Parallel and Vector Scientific Computing by Ronald W. Shonkwiler


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