Metode Monte Carlo: Perbedaan antara revisi

Deterministic methods of [[numerical integration]] operate by taking a number of evenly spaced samples from a function. In general, this works very well for functions of one variable. However, for functions of [[vector space|vector]]s, deterministic quadrature methods can be very inefficient. To numerically integrate a function of a two-dimensional vector, equally spaced grid points over a two-dimensional surface are required. For instance a 10x10 grid requires 100 points. If the vector has 100 dimensions, the same spacing on the grid would require 10¹⁰⁰ points –– that's far too many to be computed. 100 [[dimension]]s is by no means unreasonable, since in many physical problems, a "dimension" is equivalent to a [[degrees of freedom (physics and chemistry)|degree of freedom]].

Monte Carlo methods provide a way out of this exponential time-increase. As long as the function in question is reasonably [[well-behaved]], it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these points. By the [[central limit theorem]], this method will display <math>1/\sqrt{N}</math> convergence &ndash;– i.e. quadrupling the number of sampled points will halve the error, regardless of the number of dimensions.

* Tarantola, Albert, ''Inverse Problem Theory'' ([http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.html versi PDF bebas]), Society for Industrial and Applied Mathematics, 2005. ISBN 08987157250-89871-572-5