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[Link] Fibonacci Numbers In Numerical Integration

Post icon  Posted 22 June 2013 - 12:04 PM


Today I needed to use Fibonacci numbers to solve a problem at work. Fibonacci numbers are great fun, but I donít recall needing them in an applied problem before.

I needed to compute a series of integrals of the form

    f(x, y) = x^a (1-x)^b y^c (1-y)^d p(x, y)

over the unit square for a statistical application. The function p(x, y) is a little complicated but its specific form is not important here. If the constants a, b, c, and d are all positive, as they usually are in my application, the integrand can be extended to a continuous periodic function in the plane. Lattice rules are efficient for such integration problems, and the optimal lattice rules for two-variable integration are given by Fibonacci lattice rules.


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