Numerical Integration in two and Three Dimensions
نویسندگان
چکیده
منابع مشابه
Numerical Integration In many dimensions . I
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 pr...
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A high-accuracy prescription (quadrature rule) is the set of points Xj and weights Wj such that the error E (n) is a small and rapidly decreasing function of n, the number of mesh points used. Now suppose we want to integrate a function F(X l ,x2'''''Xd) = F(x) over the d-dimensional cube. The direct product technique would be to use the rule (1) d timesi ". n2 "d L L '" L Wj, Wh ... wjdF (Xj" ...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1967
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/10.2.202