Applied Parallel Computing. State of the Art in Scientific by Richard P. Brent (auth.), Jack Dongarra, Kaj Madsen, Jerzy

By Richard P. Brent (auth.), Jack Dongarra, Kaj Madsen, Jerzy Waśniewski (eds.)

Introduction The PARA workshops some time past have been dedicated to parallel computing tools in technology and know-how. there were seven PARA conferences to this point: PARA’94, PARA’95 and PARA’96 in Lyngby, Denmark, PARA’98 in Umea, ? Sweden, PARA 2000 in Bergen, N- method, PARA 2002 in Espoo, Finland, and PARA 2004 back in Lyngby, Denmark. The ?rst six conferences featured lectures in sleek numerical algorithms, desktop technological know-how, en- neering, and commercial purposes, all within the context of scienti?c parallel computing. This assembly within the sequence, the PARA 2004 Workshop with the name “State of the artwork in Scienti?c Computing”, was once held in Lyngby, Denmark, June 20–23, 2004. The PARA 2004 Workshop was once geared up by way of Jack Dongarra from the collage of Tennessee and Oak Ridge nationwide Laboratory, and Kaj Madsen and Jerzy was once ´niewski from the Technical college of Denmark. The emphasis right here used to be shifted to high-performance computing (HPC). the continued improvement of ever extra complex pcs presents the opportunity of fixing more and more dif?cult computational difficulties. notwithstanding, given the complexity of contemporary computing device architectures, the duty of understanding this capability wishes cautious realization. for instance, the failure to take advantage of a computer’s reminiscence hello- archy can degrade functionality badly. a chief drawback of HPC is the improvement of software program that optimizes the functionality of a given machine. The excessive expense of cutting-edge pcs might be prohibitive for plenty of places of work, specially if there's basically an occasional want for HPC.

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Extra info for Applied Parallel Computing. State of the Art in Scientific Computing: 7th International Workshop, PARA 2004, Lyngby, Denmark, June 20-23, 2004. Revised Selected Papers

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However, this is not to say that we should avoid the PBLAS layer. 1 and 4, as applied LU = P A factorization, are recent results obtained with Sid Chatterjee, Jim Sexton and mainly John Gunnels. 72 TFlops in the fall of 2004 that placed IBM number one in the TOP500 list. 2. References 1. R. C. Agarwal, F. G. Gustavson. A Parallel Implementation of Matrix Multiplication and LU factorization on the IBM 3090. 5 Working Group on Aspects of Computation on Asychronous Parallel Processors, book, Margaret Wright, ed.

TRSM Operation. First, we consider solving AX = C, where X overwrites C. A of size m × m is upper triangular, and C and X are m × n. Depending on m and n, there are several alternatives for doing a recursive splitting. Two of them are illustrated below. Case 1 (1 ≤ m ≤ n/2). Split C by columns only, A X1 X2 = C1 C2 , or, equivalently, AX1 = C1 , AX2 = C2 . Case 2 (1 ≤ n ≤ m/2). Split A, which is assumed to be upper triangular, by rows and columns. Since the number of right-hand sides n is much smaller than m, C is split by rows only, X1 C1 A11 A12 = , A22 X2 C2 or, equivalently, A11 X1 = C1 − A12 X2 , A22 X2 = C2 .

The TLB contains a finite set of pages. These pages are known as the current working set of New Generalized Data Structures for Matrices 15 the computation. If the computation addresses only memory in the TLB then there is no penalty. Otherwise, a TLB miss occurs resulting in a large performance penalty; see [2]. Cache blocking reduces traffic between the memory and cache. Analogously, register blocking reduces traffic between cache and the registers of the CPU. Cache and register blocking are further discussed in [2].

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