25 February 2008  12:10:24.489 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_o8_x.txt".
  Quadrature rule W file = "cheby2_o8_w.txt".
  Quadrature rule R file = "cheby2_o8_r.txt".
  Maximum degree to check =       18
 
  Spatial dimension =        1
  Number of points  =        8
 
  The quadrature rule to be tested is
  a Gauss-Chebyshev type 2 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)).
 
  Weights W:
 
  w( 1) =   0.4083294770910712E-01
  w( 2) =   0.1442256007956728    
  w( 3) =   0.2617993877991495    
  w( 4) =   0.3385402270935190    
  w( 5) =   0.3385402270935190    
  w( 6) =   0.2617993877991494    
  w( 7) =   0.1442256007956728    
  w( 8) =   0.4083294770910708E-01
 
  Abscissas X:
 
  x( 1) =  -0.9396926207859084    
  x( 2) =  -0.7660444431189779    
  x( 3) =  -0.4999999999999998    
  x( 4) =  -0.1736481776669303    
  x( 5) =   0.1736481776669304    
  x( 6) =   0.5000000000000001    
  x( 7) =   0.7660444431189780    
  x( 8) =   0.9396926207859084    
 
  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 =       15
 
          Error          Degree
 
        0.0000000000000001    0
        0.0000000000000000    1
        0.0000000000000000    2
        0.0000000000000001    3
        0.0000000000000000    4
        0.0000000000000000    5
        0.0000000000000001    6
        0.0000000000000000    7
        0.0000000000000000    8
        0.0000000000000000    9
        0.0000000000000002   10
        0.0000000000000000   11
        0.0000000000000003   12
        0.0000000000000000   13
        0.0000000000000005   14
        0.0000000000000000   15
        0.0006993006993000   16
        0.0000000000000000   17
        0.0032908268202379   18
 
INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.
 
25 February 2008  12:10:24.496 PM