# Monte Carlo Algorithm

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A Monte Carlo Algorithm is a randomized deterministic running-time approximation algorithm with a typically small error probability.

## References

### 2016

• (Wikipedia, 2016) ⇒ http://wikipedia.org/wiki/Monte_Carlo_algorithm Retrieved:2016-1-28.
• In computing, a Monte Carlo algorithm is a randomized algorithm whose running time is deterministic, but whose output may be incorrect with a certain (typically small) probability.

The related class of Las Vegas algorithms are also randomized, but in a different way: they take an amount of time that varies randomly, but always produce the correct answer. A Monte Carlo algorithm can be converted into a Las Vegas algorithm whenever there exists a procedure to verify that the output produced by the algorithm is indeed correct. If so, then the resulting Las Vegas algorithm is merely to repeatedly run the Monte Carlo algorithm until one of the runs produces an output that can be verified to be correct.

### 2009

• http://en.wikipedia.org/wiki/Monte_Carlo_method
• Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm.

Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business. These methods are also widely used in mathematics: a classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions. It is a widely successful method in risk analysis when compared with alternative methods or human intuition. When Monte Carlo simulations have been applied in space exploration and oil exploration, actual observations of failures, cost overruns and schedule overruns are routinely better predicted by the simulations than by human intuition or alternative "soft" methods.

The term "Monte Carlo method" was coined in the 1940s by physicists working on nuclear weapon projects in the Los Alamos National Laboratory.