01 March 2008 12:11:29 PM

CHEBYSHEV2_RULE
  C++ version

  Compiled on Mar  1 2008 at 12:10:50.

  Compute a Gauss-Chebyshev type 2 rule for approximating

    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx

  of order ORDER.

  The user specifies ORDER and OUTPUT.

  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

  OUTPUT option is "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Chebyshev type 2 quadrature rule.
%  ORDER = 8
%
%  Standard rule:
%    Integral ( -1 <= x <= +1 ) f(x) * sqrt ( 1 - x^2 ) dx
%    is to be approximated by
%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
  w(1) = 0.04083294770910712;
  w(2) = 0.1442256007956728;
  w(3) = 0.2617993877991495;
  w(4) = 0.338540227093519;
  w(5) = 0.338540227093519;
  w(6) = 0.2617993877991494;
  w(7) = 0.1442256007956728;
  w(8) = 0.04083294770910708;

  x(1) = -0.9396926207859083;
  x(2) = -0.7660444431189779;
  x(3) = -0.4999999999999998;
  x(4) = -0.1736481776669303;
  x(5) = 0.1736481776669304;
  x(6) = 0.5000000000000001;
  x(7) = 0.766044443118978;
  x(8) = 0.9396926207859084;

  r(1) = -1;
  r(2) = 1;

CHEBYSHEV1_RULE:
  Normal end of execution.

01 March 2008 12:11:29 PM