Monte Carlo integration

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Monte Carlo integration
It is a numerical probabilistic algorithm
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MCint(f,n,a,b) sum 0 For i 1 to n do x
uniform(a,b) sum sum f(x) Return ( b-a)
(sum/n)
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Variance of the estimate is inverse proportion to
n The expected error is proportion to
A deterministic algorithm for integration will
sample at regular interval.
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DETint(f,n,a,b) sum 0 delta (b-a)/n x a
delta/2 For I 1 to n do sum sum f(x) x
x delta Return sum delta
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Advantage of MCint when doing multiple integral
in high dimension. As the sample point increases
exponentially with the dimension. Example 100,
100x100, 100x100x100. MCint is faster than a
deterministic algorithm for dimension gt 4.