Simpsons rule relies on formulae that are applicable

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Unformatted text preview: ous on [a, b] and f ≤ M ∀x ∈ [a, b], then b max Tn − x∈[a,b] a M (b − a)3 f (x)dx ≤ . 12 • What is wrong eith the above theorem in the case that f (x) ≡ Q(x, ω )? March 3, 2003 Stochastic Programming – Lecture 14 Slide 9 Numerical Integration • Q (x, ω ) doesn't exist. • If you want to know more about numerical integration, the buzzwords are... Numerical quadrature, Simpson's rule... • Numerical integration really only works well in small dimension. (Simpson's rule relies on formulae that are applicable or accurate only in dimenions say ≤ 10 or 12. • For some special cases (like simple recourse), it might be possible to use numerical integration for your stochastic programming problem. March 3, 2003 Stochastic Programming – Lecture 14 Slide 10 March 3, 2003 Stochastic Programming – Lecture 14 Slide 11   ¡ ©¡ ¡©¡ ¡ ©¡ ¡¡¡©¡©¡¡©¡©¡¡¡¡¡¡¡¡¡¡¡¡©¡©¡©¡©¡©¡©¡©¡©¡©¡¡ ¡ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡...
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