Sequential Monte Carlo techniques for the solution of linear systems
Journal of Scientific Computing
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Parallel resolvent Monte Carlo algorithms for linear algebra problems
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Parallel Quasi-Monte Carlo Integration Using (t, s)-Sequences
ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
Matrix Computations Using Quasirandom Sequences
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
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This paper presents a parallel quasi-Monte Carlo method for solving general sparse systems of linear algebraic equations. In our parallel implementation we use disjoint contiguous blocks of quasirandom numbers extracted from a given quasirandom sequence for each processor. In this case, the increased speed does not come at the cost of less thrust-worthy answers. Similar results have been reported in the quasi-Monte Carlo literature for parallel versions of computing extremal eigenvalues [8] and integrals [9]. But the problem considered here is more complicated - our algorithm not only uses an s-dimensional quasirandom sequence, but also its k-dimensional projections (k = 1,2, . . ., s-1) onto the coordinate axes. We also present numerical results. In these test examples of matrix equations, the martrices are sparse, randomly generated with condition numbers less than 100, so that each corresponding Neumann series is rapidly convergent. Thus we use quasirandom sequences with dimension less than 10.