Comparing numerical dimensions

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...

Numerical Relativity in 3+1 Dimensions

Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest are briefly reviewed: binary black hole mergers, the evolution of strong gravitational waves, and shift conditions for neutron star binaries.

Accurate Numerical Fourier Transform in d-Dimensions

A Rigorous Numerical Method in Infinite Dimensions

Date Approved For my mother, in loving memory iii ACKNOWLEDGEMENTS The following are examples of the many people whose support has been instrumental in my completing this thesis. Joe, who offered technical, canine, and brotherly support; Becky, my wonderful and crazy sister; Dad, who accepted that in my case math wins out over physics; Mom, my favorite role model and confidante, who explained t...

Numerical integration in many dimensions . II

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" ...