By Greg Astfalk
Protecting functions on complex structure pcs, this quantity brings jointly up-to-date types of 30 articles that initially seemed in "SIAM information" from 1990 to 1995.
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FIG. 1. Empirical comparison of the Jacobi method, red-black Gauss-Seidel method, optimal red-black SOR method, the backward random walk method, and the nonlinear quotient method (which is the expected value of the backward method). For the random walk method, iteration number refers to maximal length of random walks. 2. 33 Concluding Comments It is well known that these Monte Carlo methods are far inferior to many deterministic methods for these types of problems. However, in very high dimensions variants of these Monte Carlo methods are often used to solve problems in quantum mechanics.
Finally, we consider the cost of generating each sample. Since our algorithm advances walkers from the interior until they hit the boundary, we average one sample every TQ^ (the average length of a walk) iterations per walker. We will refer to this algorithm as the MIMD or "forward" random walk algorithm. In contrast, the choice of mapping grid points onto the processor of a massively parallel SIMD machine, such as the CM-2 or MP-2, leads to a different set of considerations. In fact, the algorithm described above is an extremely poor choice on a SIMD machine.
1. Illustration of plaquette calculation. of the lattice. Nsa and A^a are the spatial and the temporal extents of the lattice, respectively. 1. 2, where g is the coupling between the gauge fields. The action for the quarks is where M is a large sparse matrix the size of the lattice squared. In particular, we use the Wilson quark representation, in which M is given by where K — l/2m, with m being the quark mass, 7^ are the Dirac gamma matrices, and one can choose r = I . For state-of-the-art simulations the lattice size N = 324, and with i/j having four spin and three color complex components, M is a (24 x 1048576) x (24 x 1048576) matrix.