>> chebyshev1_rule ( 8, 'MAT' )
01-Mar-2008 17:18:58

CHEBYSHEV1_RULE
  MATLAB version

  Compute a Gauss-Chebyshev type 1 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 = "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Chebyshev type 1e 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) =       0.3926990816987241;
  w(2) =       0.3926990816987241;
  w(3) =       0.3926990816987241;
  w(4) =       0.3926990816987241;
  w(5) =       0.3926990816987241;
  w(6) =       0.3926990816987241;
  w(7) =       0.3926990816987241;
  w(8) =       0.3926990816987241;

  x(1) =      -0.9807852804032304;
  x(2) =      -0.8314696123025453;
  x(3) =      -0.5555702330196020;
  x(4) =      -0.1950903220161282;
  x(5) =       0.1950903220161283;
  x(6) =       0.5555702330196023;
  x(7) =       0.8314696123025452;
  x(8) =       0.9807852804032304;

  r(1) =      -1.0000000000000000;
  r(2) =       1.0000000000000000;

CHEBYSHEV1_RULE:
  Normal end of execution.

01-Mar-2008 17:18:58
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