19 January 2008 12:23:12 PM

GEN_HERMITE_RULE
  C++ version

  Compiled on Jan 19 2008 at 12:02:33.

  Compute a generalized Gauss-Hermite rule for approximating

    Integral ( -oo < x < oo ) |X|^ALPHA exp(-x^2) f(x) dx

  of order ORDER and parameter ALPHA.

  The user specifies ORDER, ALPHA, OPTION, and OUTPUT.

  OPTION is:

    0 to get the standard rule for handling:
      Integral ( -oo < x < oo ) |x|^ALPHA exp(-x^2) f(x) dx

    1 to get the modified rule for handling:
      Integral ( -oo < x < oo )                   f(x) dx

    For OPTION = 1, the weights of the standard rule
    are divided by |x|^ALPHA * exp(-x^2).

  OUTPUT is:

  "C++" for printed C++ output;
  "F77" for printed Fortran77 output;
  "F90" for printed Fortran90 output;
  "MAT" for printed MATLAB output;

  or:

  "filename" to generate 3 files:

    filename_w.txt - the weight file
    filename_x.txt - the abscissa file.
    filename_r.txt - the region file.

  The requested order of the rule is = 8

  The requested ALPHA = 3

  The requested value of OPTION = 0

  OUTPUT option is "MAT".
%
%  Weights W, abscissas X and range R
%  for a generalized Gauss-Hermite quadrature rule
%  ORDER = 8
%  ALPHA = 3
%
%  OPTION = 0, Standard rule:
%   Integral ( -oo < x < oo ) |x|^ALPHA exp(-x^2) f(x) dx
%   is to be approximated by
%   sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
  w(1) = 0.0006579248431516193;
  w(2) = 0.03708889236552609;
  w(3) = 0.2388178861819341;
  w(4) = 0.2234352966093881;
  w(5) = 0.2234352966093881;
  w(6) = 0.2388178861819341;
  w(7) = 0.03708889236552609;
  w(8) = 0.0006579248431516193;

  x(1) = -3.309666797833763;
  x(2) = -2.393988043347147;
  x(3) = -1.603631817982631;
  x(4) = -0.8621437977399313;
  x(5) = 0.8621437977399313;
  x(6) = 1.603631817982631;
  x(7) = 2.393988043347147;
  x(8) = 3.309666797833763;

  r(1) = -1e+30;
  r(2) = 1e+30;

GEN_LAGUERRE_RULE:
  Normal end of execution.

19 January 2008 12:23:12 PM