Papers › An algorithm for estimating volumes and other integrals in n dimensions
An algorithm for estimating volumes and other integrals in n dimensions
Arun I., Murugesan Venkatapathi
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The computational cost in evaluation of the volume of a body using numerical integration grows exponentially with dimension of the space n. The most generally applicable algorithms for estimating n-volumes and integrals are based on Markov Chain Monte Carlo (MCMC) methods, and they are suited for convex domains. We analyze a less known alternate method used for estimating n-dimensional volumes, that is agnostic to the convexity and roughness of the body. It results due to the possible decomposition of an arbitrary n-volume into an integral of statistically weighted volumes of n-spheres. We establish its dimensional scaling, and extend it for evaluation of arbitrary integrals over non-convex domains. Our results also show that this method is significantly more efficient than the MCMC approach even when restricted to convex domains, for n ∼< 100. An importance sampling may extend this advantage to larger dimensions.
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