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)
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Polynomial arithmetic analogue of Halton sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Regarding test functions for multi-dimensional integration
ACM SIGNUM Newsletter
Quadrature formulas for multivariate convex functions
Journal of Complexity
A Nested Partitioning Procedure for Numerical Multiple Integration
ACM Transactions on Mathematical Software (TOMS)
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
ACM Transactions on Mathematical Software (TOMS)
Quasi-Monte Carlo methods in cash flow testing simulations
Proceedings of the 32nd conference on Winter simulation
Generating "dependent" quasi-random numbers
Proceedings of the 32nd conference on Winter simulation
A Novel Sampling Approach to Combinatorial Optimization Under Uncertainty
Computational Optimization and Applications
Induced well-distributed sets in Riemannian spaces
ACM Transactions on Mathematical Software (TOMS)
Parallel and Distributed Computing Issues in Pricing Financial Derivatives through Quasi Monte Carlo
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
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
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Adaptive sampling and modeling of analog circuit performance parameters with pseudo-cubic splines
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Hierarchical performance macromodels of feasible regions for synthesis of analog and RF circuits
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Numerical integration in logistic-normal models
Computational Statistics & Data Analysis
Research Note: Generating parallel quasirandom sequences via randomization
Journal of Parallel and Distributed Computing
Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Efficient uncertainty quantification with the polynomial chaos method for stiff systems
Mathematics and Computers in Simulation
Generalized Halton sequences in 2008: A comparative study
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy
Journal of Computational and Applied Mathematics
On the optimal Halton sequence
Mathematics and Computers in Simulation
Using XCS to describe continuous-valued problem spaces
IWLCS'03-05 Proceedings of the 2003-2005 international conference on Learning classifier systems
Collocation least-squares polynomial chaos method
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
A model framework for greedy routing in a sensor network with a stochastic power scheme
ACM Transactions on Sensor Networks (TOSN)
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
Journal of Computational Physics
Web-Services based modelling/optimisation for engineering design
OTM'05 Proceedings of the 2005 OTM Confederated international conference on On the Move to Meaningful Internet Systems
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Density-controlled sampling of parametric surfaces using adaptive space-filling curves
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
Maximum likelihood estimation from interval censored recurrent event data
Computers and Industrial Engineering
Journal of Computational Physics
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The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are shown to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.