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 vast context of parallelism. The authors commence by way of giving the reader a deeper knowing of the problems via a basic exam of timing, info dependencies, and conversation. those principles are applied with appreciate to shared reminiscence, parallel and vector processing, and disbursed reminiscence cluster computing. Threads, OpenMP, and MPI are lined, besides code examples in Fortran, C, and Java. the rules of parallel computation are utilized all through because the authors disguise conventional themes in a primary direction in medical computing. development at the basics of floating element illustration and numerical blunders, a radical 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, similar to Monte Carlo tools.

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**Example text**

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. Powers – Russian Peasant Algorithm For a number a and a positive integer n, we want to compute all of its powers up to a n . This is like the partial sums problem above, for products instead of sums, except that all terms of the sequence are the same, being equal to a. Appropriately, a simpler algorithm does the job. The algorithm described below is called the “Russian Peasant Algorithm” because it is similar to a multiplication technique of the same name.

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. Powers – Russian Peasant Algorithm For a number a and a positive integer n, we want to compute all of its powers up to a n . This is like the partial sums problem above, for products instead of sums, except that all terms of the sequence are the same, being equal to a.

2 Some Basic Complexity Calculations Vector Operation As our first example, consider a vector operation such as the component by component addition of two vectors of size n. Given n processors, this can be done in one time step as follows: assign processor i to add the components xi + yi in parallel with the other processors (see Fig. 13). So T∞ = 1. Obviously T1 = n and so SUn = n and E Fn = n/n = 1. Reduction It is often necessary to derive a scalar value from a vector, one which depends on all the components of the vector.

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

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