20 May 2009 12:52:03 AM

HERMITE_RULE
  C++ version

  Compiled on May 20 2009 at 00:45:39.

  Compute a Gauss-Hermite quadrature rule for approximating

    Integral ( -oo < x < +oo ) w(x) f(x) dx

  of order ORDER.

  The user specifies ORDER, OPTION, and OUTPUT.

  OPTION specifies the weight function w(x):

    0, the unweighted rule for:
      Integral ( -oo < x < +oo )             f(x) dx

    1, the physicist weighted rule for:
      Integral ( -oo < x < +oo ) exp(-x*x)   f(x) dx

    2, the probabilist weighted rule for:
      Integral ( -oo < x < +oo ) exp(-x*x/2) f(x) dx

  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.

  ORDER =  8
  OPTION = 1
  OUTPUT = "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Hermite quadrature rule
%  ORDER = 8
%
%  OPTION = 1, physicist weighted rule:
%    Integral ( -oo < x < +oo ) exp(-x*x) f(x) dx
%    is to be approximated by
%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
  w(1) = 0.0001996040722107464;
  w(2) = 0.01707798300736032;
  w(3) = 0.207802325814245;
  w(4) = 0.6611470125561838;
  w(5) = 0.6611470125561838;
  w(6) = 0.207802325814245;
  w(7) = 0.01707798300736032;
  w(8) = 0.0001996040722107464;

  x(1) = -2.930637420257244;
  x(2) = -1.981656756695843;
  x(3) = -1.15719371244678;
  x(4) = -0.3811869902073221;
  x(5) = 0.3811869902073221;
  x(6) = 1.15719371244678;
  x(7) = 1.981656756695843;
  x(8) = 2.930637420257244;

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

HERMITE_RULE:
  Normal end of execution.

20 May 2009 12:52:03 AM