Parallel Importance Separation and Adaptive Monte Carlo Algorithms for Multiple Integrals

• Ivan Dimov
• Aneta Karaivanova
• Rayna Georgieva
• Sofiya Ivanovska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)

Abstract

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.

Keywords

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Authors and Affiliations

• Ivan Dimov
• 1
• Aneta Karaivanova
• 1
• Rayna Georgieva
• 1
• Sofiya Ivanovska
• 1 