An adaptive algorithm for the approximate calculation of multiple integrals
ACM Transactions on Mathematical Software (TOMS)
Parallel globally adaptive algorithms for multi-dimensional integration
Applied Numerical Mathematics - Special issue on massively parallel computing and applications
Optimally combining sampling techniques for Monte Carlo rendering
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Robust monte carlo methods for light transport simulation
Robust monte carlo methods for light transport simulation
Adaptive sampling for efficient failure probability analysis of SRAM cells
Proceedings of the 2009 International Conference on Computer-Aided Design
Parallel Monte Carlo approach for integration of the rendering equation
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
A superconvergent monte carlo method for multiple integrals on the grid
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
| Hi-index | 0.00 |
Monte Carlo Method (MCM) is the only viable method for many high-dimensional problems since its convergence is independent of the dimension. In this paper we develop an adaptive Monte Carlo method based on the ideas and results of the importance separation, a method that combines the idea of separation of the domain into uniformly small subdomains with the Kahn approach of importance sampling. We analyze the error and compare the results with crude Monte Carlo and importance sampling which is the most widely used variance reduction Monte Carlo method. We also propose efficient parallelizations of the importance separation method and the studied adaptive Monte Carlo method. Numerical tests implemented on PowerPC cluster using MPI are provided.