| R. De Leone and O. L. Mangasarian. Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem. Mathematical Programming, 42(2):347--361, November 1988. |
....However, having fewer wavefronts still improves performance by reducing the total barrier synchronization overhead and also the load imbalance within each wavefront. Finally, we note that there are explicitly parallel algorithms which do not correspond to the parallelization of serial algorithms [6, 14]. Since our focus is mainly the parallelization of loops specified in sequential programming languages such as Fortran D [7] these algorithms do not fall into the scope of this paper. 1.4 Paper Organization The remainder of this paper is organized as follows. Section 2 explains the methods we ....
R. De Leone and O. L. Mangasarian. Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem. Mathematical Programming, 42(2):347--361, November 1988.
....point of view, and it does not specify any explicit directives for hardware. However, there are some disadvantages of defining a weakly ordered system in this manner. First, the operation of algorithms that are inherently asynchronous and do not rely on sequential consistency for correctness [DeM88] is left unspecified. This disadvantage is easily handled by implementing weakly ordered systems so that for such algorithms, reasonable results are obtained. Second, programmers may wish to debug programs on a weakly ordered system that do not (yet) fully obey the synchronization model. One ....
R. De Leone and O. L. Mangasarian, Asynchronous Parallel Successive Overrelaxation for the Symmetric Linear Complementarity Problem, Mathematical Programming 42(1988), 347-361.
.... the array z Barrier Serial check to see if further relaxation is necessary The SOR (Successive Over Relaxation) method is used to solve the symmetric linear complementarity problem M z q 0, z 0, z (M z q) 0 A particular version of asynchronous SOR is used for analysis [42]. Matrix M is a read only sparse matrix. Elements of the matrix are compressed and stored in an array, with separate arrays to store the row and column indices. Data elements in the array z are dynamically selected by each processor and updated, and the new values computed by processors are made ....
R. De Leone and O. L. Mangasarian, "Asynchronous Parallel Successive Overrelaxation For The Symmetric Linear Complementarity Problem," Computer Sciences Technical Report #755, University of Wisconsin-Madison, Madison, WI 53706, Feb. 1988.
....to be classified as synchronizing operations for correctness. The semantics of data races is well defined by the partial order semantics of program execution under the LC model. These properties of the LC model are consistent with the assumptions made by designers of asynchronous algorithms [7]. From the previous examples, one can imagine several situations in which the SC model prevents the use of instruction reordering, an optimization that is commonly used in compilers and in uniprocessor hardware. For example, in Figure 1 the result r1 = r2 = 0 is prohibited by sequential ....
R. De Leone and O. L. Mangasarian. Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem. Mathematical Programming, 42(2):347-- 361, November 1988.
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