Download e-book for iPad: An Introduction to Parallel and Vector Scientific Computing by Ronald W. Shonkwiler

By Ronald W. Shonkwiler

ISBN-10: 0521683378

ISBN-13: 9780521683371

ISBN-10: 052186478X

ISBN-13: 9780521864787

During this textual content, scholars of utilized arithmetic, technological know-how and engineering are brought to basic methods of considering the vast context of parallelism. The authors start via giving the reader a deeper figuring out of the problems via a basic exam of timing, facts dependencies, and communique. those rules are carried out with admire to shared reminiscence, parallel and vector processing, and disbursed reminiscence cluster computing. Threads, OpenMP, and MPI are lined, in addition to code examples in Fortran, C, and Java. the rules of parallel computation are utilized all through because the authors conceal conventional subject matters in a primary direction in clinical computing. development at the basics of floating element illustration and numerical mistakes, an intensive remedy of numerical linear algebra and eigenvector/eigenvalue difficulties is supplied. through learning how those algorithms parallelize, the reader is ready to discover parallelism inherent in different computations, equivalent to Monte Carlo tools.

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Extra resources for An Introduction to Parallel and Vector Scientific Computing

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Using 1 processor, T1 = n − 1 and, using p = n/2 processors (in the last step), T∞ = Tn/2 = r = log n . The speedup n−1 is SU (n/2) = log , and the efficiency is E f = n2(n−1) . n log n Matrix Powers For a given square matrix A of size m × m, we want to calculate its powers A2 through An . Again, if n is a power of 2, we proceed as in Fig. 15. However, now the multiplication at each node is a matrix–matrix product by square matrices of size m × m. 3 we will consider matrix–matrix products in detail and examine various computational possibilities for the calculation.

P, and then the arcs are (1, 2), (2, 3), . . , ( p − 1, p), and ( p, 1). The number of links incident at any node is 2. The diameter of the network is ( p − 1)/2 and the connectivity is 2. Since both links at every node can be in use simultaneously and in both directions, the time for a multinode broadcast is also ( p − 1)/2. Mesh The mesh topology is popular because for many problems it mimics the geometry of physical space. In a d-dimensional mesh, the nodes are conceptually arrayed on the points of a d-dimensional space having integer coordinates.

In reality, the 0s need not be added of course. For example, in summing n = 5 numbers, during the first time step the additions a1 = a1 + a2 and a2 = a3 + a4 take place; a5 is not involved yet. Next in step 2, a1 = a1 + a2 , and finally in the third step, sum = a1 + a5 . Hence 3 steps are required, one more than the two required in summing four addends. Recursive Doubling Given a finite sequence of numbers, a1 , a2 , . . , an , compute the sequence of all partial sums (or all partial products), s1 = a1 s2 = a 1 + a 2 ..

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

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