Numerical Integration In many dimensions . I
نویسنده
چکیده
If a d-dimensional integral involves an integrand ofthe functional form F (II (x I) + f2(X2) + ... ), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates XI to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and practical numerical approach to a number of problems of interest. Among the examples studied is the computation of the volume of phase space for an arbitrary collection of relativistic particles. One important aspect of the approach involves numerical integration along various contours in the complex plane.
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