Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Parallel resolvent Monte Carlo algorithms for linear algebra problems
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Iterative Monte Carlo Algorithms for Linear Algebra Problems
WNAA '96 Proceedings of the First International Workshop on Numerical Analysis and Its Applications
Matrix Computations Using Quasirandom Sequences
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Sequential Monte Carlo Techniques for the Solution of Linear Systems
Sequential Monte Carlo Techniques for the Solution of Linear Systems
Monte Carlo and Quasi-Monte Carlo Algorithms for the Barker-Ferry Equation with Low Complexity
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
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In this paper we analyze a quasi-Monte Carlo method for solving systems of linear algebraic equations. It is well known that the convergence of Monte Carlo methods for numerical integration can often be improved by replacing pseudorandom numbers with more uniformly distributed numbers known as quasirandom numbers. Here the convergence of a Monte Carlo method for solving systems of linear algebraic equations is studied when quasirandom sequences are used. An error bound is established and numerical experiments with large sparse matrices are performed using Sobol, Halton and Faure sequences. The results indicate that an improvement in both the magnitude of the error and the convergence rate are achieved.