A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues
نویسندگان
چکیده
1 Florida State University, Department of Computer Science, Tallahassee, FL 32306-4530, USA 2 Bulgarian Academy of Sciences, Central Laboratory for Parallel Processing, 1113 Sofia, Bulgaria Abstract The convergence of Monte Carlo methods for numerical integration can often be improved by replacing pseudorandom numbers (PRNs) with more uniformly distributed numbers known as quasirandom numbers (QRNs). In this paper the convergence of a Monte Carlo method for evaluating the extremal eigenvalues of a given matrix is studied when quasirandom sequences are used. An error bound is established and numerical experiments with large sparse matrices are performed using three different QRN sequences: Soboĺ, Halton and Faure. The results indicate:
منابع مشابه
A Parallel Quasi-Monte Carlo Method for Solving Systems of Linear Equations
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 report...
متن کاملTwo and Three Dimensional Monte Carlo Simulation of Magnetite Nanoparticle Based Ferrofluids
We have simulated a magnetite nanoparticle based ferrofluid using Monte Carlo method. Two and three dimensional Monte Carlo simulations have been done using parallel computing technique. The aggregation and rearrangement of nanoparticles embedded in a liquid carrier have been studied in various particle volume fractions. Our simulation results are in complete agreement with the reported experim...
متن کاملParallel Quasi-Monte Carlo Integration by Partitioning Low Discrepancy Sequences
A general concept for parallelizing quasi-Monte Carlo methods is introduced. By considering the distribution of computing jobs across a multiprocessor as an additional problem dimension, the straightforward application of quasiMonte Carlo methods implies parallelization. The approach in fact partitions a single low-discrepancy sequence into multiple low-discrepancy sequences. This allows for ad...
متن کاملDomain Decomposition Solution of Elliptic Boundary-Value Problems via Monte Carlo and Quasi-Monte Carlo Methods
Domain decomposition of two-dimensional domains on which boundary-value elliptic problems are formulated, is accomplished by probabilistic (Monte Carlo) as well as by quasi-Monte Carlo methods, generating only few interfacial values and interpolating on them. Continuous approximations for the trace of solution are thus obtained, to be used as boundary data for the sub-problems. The numerical tr...
متن کاملParallel and Distributed Computing Issues in Pricing Financial Derivatives through Quasi Monte Carlo
Monte Carlo (MC) techniques are often used to price complex financial derivatives. The computational effort can be substantial when high accuracy is required. However, MC computations are latency tolerant, and are thus easy parallelize even with high communication overheads, such as in a distributed computing environment. A drawback of MC is its relatively slow convergence rate, which can be ov...
متن کامل