Monte Carlo Method – 몬테카를로법

Monte Carlo method

A Monte Carlo method is a computational algorithm which relies on repeated random sampling to compute its results. Monte Carlo methods are often used when simulating physical and mathematical systems. Because of their reliance on repeated computation and random or pseudo-random numbers, Monte Carlo methods are most suited to calculation by a computer. Monte Carlo methods tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm.

몬테카를로 법(Monte Carlo method)은, 물리적, 수학적 시스템의 행동을 시뮬레이션하기 위한 계산 알고리즘이다. 다른 알고리즘과는 달리 통계학적이고, 일반적으로 무작위의 숫자를 사용한 비결정적인 방법이다. 스타니스와프 울람이 모나코의 유명한 도박의 도시 몬테카를로의 이름을 본따 명명하였다.

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 몬테카를로 방법

Monte Carlo integration

In mathematics, Monte Carlo integration is numerical quadrature using pseudorandom numbers.
That is, Monte Carlo integration methods are algorithms for the approximate evaluation of definite integrals,
usually multidimensional ones.
The usual algorithms evaluate the integrand at a regular grid.
Monte Carlo methods, however, randomly choose the points at which the integrand is evaluated.

Informally, to estimate the area of a domain D, first pick a simple domain d whose area is easily calculated and which contains D. Now pick a sequence of random points that fall within d.
Some fraction of these points will also fall within D. The area of D is then estimated as this fraction multiplied by the area of d.

The traditional Monte Carlo algorithm distributes the evaluation points uniformly over the integration region. Adaptive algorithms such as VEGAS and MISER use importance sampling and stratified sampling techniques to get a better result.

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