04-Mar-2008 11:02:06

INT_EXACTNESS_CHEBYSHEV2
  MATLAB version

  Investigate the polynomial exactness of a Gauss-Chebyshev
  type 2 quadrature rule by integrating all monomials up to a given
  degree over the [-1,+1] interval.

  The rule will be adjusted to the [0,1] hypercube.

INT_EXACTNESS_CHEBYSHEV2: User input:
  Quadrature rule X file = "cheby2_o16_x.txt".
  Quadrature rule W file = "cheby2_o16_w.txt".
  Quadrature rule R file = "cheby2_o16_r.txt".
  Maximum degree to check = 35

  Spatial dimension = 1
  Number of points  = 16

  The quadrature rule to be tested is
  a Gauss-Chebyshev type 2 rule
  ORDER = 16

  Standard rule:
    Integral ( -1 <= x <= +1 ) f(x) * ( 1 - x^2 ) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

  w(1) =       0.0062395514122521
  w(2) =       0.0241155196562360
  w(3) =       0.0512136561664420
  w(4) =       0.0838742074512088
  w(5) =       0.1176861850811667
  w(6) =       0.1480830941187536
  w(7) =       0.1709596635633560
  w(8) =       0.1832262859480331
  w(9) =       0.1832262859480331
  w(10) =       0.1709596635633560
  w(11) =       0.1480830941187536
  w(12) =       0.1176861850811666
  w(13) =       0.0838742074512089
  w(14) =       0.0512136561664420
  w(15) =       0.0241155196562360
  w(16) =       0.0062395514122521

  Abscissas X:

  x(1) =      -0.9829730996839018
  x(2) =      -0.9324722294043557
  x(3) =      -0.8502171357296140
  x(4) =      -0.7390089172206593
  x(5) =      -0.6026346363792563
  x(6) =      -0.4457383557765379
  x(7) =      -0.2736629900720829
  x(8) =      -0.0922683594633019
  x(9) =       0.0922683594633020
  x(10) =       0.2736629900720830
  x(11) =       0.4457383557765384
  x(12) =       0.6026346363792564
  x(13) =       0.7390089172206592
  x(14) =       0.8502171357296141
  x(15) =       0.9324722294043558
  x(16) =       0.9829730996839018

  Region R:

  r(1) = -1.000000e+00
  r(2) = 1.000000e+00

  A Gauss-Chebyshev type 2 rule would be able to exactly
  integrate monomials up to and including 
  degree = 31

      Error    Degree

        0.0000000000000001    0
        0.0000000000000000    1
        0.0000000000000003    2
        0.0000000000000000    3
        0.0000000000000003    4
        0.0000000000000000    5
        0.0000000000000003    6
        0.0000000000000000    7
        0.0000000000000002    8
        0.0000000000000000    9
        0.0000000000000006   10
        0.0000000000000000   11
        0.0000000000000005   12
        0.0000000000000000   13
        0.0000000000000002   14
        0.0000000000000000   15
        0.0000000000000002   16
        0.0000000000000000   17
        0.0000000000000001   18
        0.0000000000000000   19
        0.0000000000000000   20
        0.0000000000000000   21
        0.0000000000000002   22
        0.0000000000000000   23
        0.0000000000000002   24
        0.0000000000000000   25
        0.0000000000000000   26
        0.0000000000000000   27
        0.0000000000000000   28
        0.0000000000000000   29
        0.0000000000000001   30
        0.0000000000000000   31
        0.0000000282824067   32
        0.0000000000000000   33
        0.0000002468282759   34
        0.0000000000000000   35

INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.

04-Mar-2008 11:02:06