25 February 2008  12:10:28.967 PM                                               
 
INT_EXACTNESS_CHEBYSHEV2
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Chebyshev
  type 2 quadrature rule by integrating weighted 
  monomials up to a given degree over the [-1,+1] interval.
 
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) * sqrt ( 1 - x^2 ) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.6239551412252139E-02
  w( 2) =   0.2411551965623602E-01
  w( 3) =   0.5121365616644202E-01
  w( 4) =   0.8387420745120885E-01
  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) =   0.8387420745120885E-01
  w(14) =   0.5121365616644197E-01
  w(15) =   0.2411551965623597E-01
  w(16) =   0.6239551412252137E-02
 
  Abscissas X:
 
  x( 1) =  -0.9829730996839018    
  x( 2) =  -0.9324722294043556    
  x( 3) =  -0.8502171357296140    
  x( 4) =  -0.7390089172206593    
  x( 5) =  -0.6026346363792563    
  x( 6) =  -0.4457383557765379    
  x( 7) =  -0.2736629900720829    
  x( 8) =  -0.9226835946330189E-01
  x( 9) =   0.9226835946330203E-01
  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) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
  A Gauss-Chebyshev type 2 rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree
 
        0.0000000000000001    0
        0.0000000000000001    1
        0.0000000000000003    2
        0.0000000000000000    3
        0.0000000000000003    4
        0.0000000000000000    5
        0.0000000000000005    6
        0.0000000000000000    7
        0.0000000000000003    8
        0.0000000000000000    9
        0.0000000000000004   10
        0.0000000000000000   11
        0.0000000000000003   12
        0.0000000000000000   13
        0.0000000000000003   14
        0.0000000000000000   15
        0.0000000000000000   16
        0.0000000000000000   17
        0.0000000000000002   18
        0.0000000000000000   19
        0.0000000000000003   20
        0.0000000000000000   21
        0.0000000000000005   22
        0.0000000000000000   23
        0.0000000000000007   24
        0.0000000000000000   25
        0.0000000000000006   26
        0.0000000000000000   27
        0.0000000000000004   28
        0.0000000000000000   29
        0.0000000000000005   30
        0.0000000000000000   31
        0.0000000282824071   32
        0.0000000000000000   33
        0.0000002468282765   34
        0.0000000000000000   35
 
INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.
 
25 February 2008  12:10:28.976 PM