Monte Carlo method

related topics
{math, number, function}
{math, energy, light}
{rate, high, increase}
{system, computer, user}
{theory, work, human}
{company, market, business}
{@card@, make, design}
{ship, engine, design}
{food, make, wine}
{film, series, show}
{mi², represent, 1st}

Data analysis · Visualization

Smoothed particle hydrodynamics

Molecular dynamics

Monte Carlo methods (or Monte Carlo experiments) 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 unfeasible or impossible to compute an exact result with a deterministic algorithm.[1]

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.[2]

The term "Monte Carlo method" was coined in the 1940s by physicists working on nuclear weapon projects in the Los Alamos National Laboratory.[3]

Contents

Full article ▸

related documents
Bessel function
Probability theory
Euler's formula
Convolution
Dual space
Fundamental theorem of algebra
Primitive recursive function
Basis (linear algebra)
Continuous function
BCH code
Ackermann function
Multivariate normal distribution
Hyperreal number
Fundamental group
Computable number
Halting problem
Fermat number
Lp space
Dynamic programming
Prime number theorem
Subset sum problem
Group action
Abelian group
Permutation
Central limit theorem
Truth table
Uniform space
Taylor series
Factorial
Frame problem