25 February 2008  12:07:00.443 PM                                               
 
INT_EXACTNESS_CHEBYSHEV1
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Chebyshev
  type 1 quadrature rule by integrating weighted 
  monomials up to a given degree over the [-1,+1] interval.
 
INT_EXACTNESS_CHEBYSHEV1: User input:
  Quadrature rule X file = "cheby1_o16_x.txt".
  Quadrature rule W file = "cheby1_o16_w.txt".
  Quadrature rule R file = "cheby1_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 1 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) =   0.1963495408493621    
  w( 2) =   0.1963495408493621    
  w( 3) =   0.1963495408493621    
  w( 4) =   0.1963495408493621    
  w( 5) =   0.1963495408493621    
  w( 6) =   0.1963495408493621    
  w( 7) =   0.1963495408493621    
  w( 8) =   0.1963495408493621    
  w( 9) =   0.1963495408493621    
  w(10) =   0.1963495408493621    
  w(11) =   0.1963495408493621    
  w(12) =   0.1963495408493621    
  w(13) =   0.1963495408493621    
  w(14) =   0.1963495408493621    
  w(15) =   0.1963495408493621    
  w(16) =   0.1963495408493621    
 
  Abscissas X:
 
  x( 1) =   0.9951847266721968    
  x( 2) =   0.9569403357322088    
  x( 3) =   0.8819212643483550    
  x( 4) =   0.7730104533627370    
  x( 5) =   0.6343932841636455    
  x( 6) =   0.4713967368259978    
  x( 7) =   0.2902846772544623    
  x( 8) =   0.9801714032956076E-01
  x( 9) =  -0.9801714032956065E-01
  x(10) =  -0.2902846772544622    
  x(11) =  -0.4713967368259977    
  x(12) =  -0.6343932841636454    
  x(13) =  -0.7730104533627370    
  x(14) =  -0.8819212643483549    
  x(15) =  -0.9569403357322088    
  x(16) =  -0.9951847266721968    
 
  Region R:
 
  r( 1) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
  A Gauss-Chebyshev type 1 rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree
 
        0.0000000000000004    0
        0.0000000000000001    1
        0.0000000000000000    2
        0.0000000000000001    3
        0.0000000000000000    4
        0.0000000000000001    5
        0.0000000000000002    6
        0.0000000000000001    7
        0.0000000000000001    8
        0.0000000000000001    9
        0.0000000000000001   10
        0.0000000000000001   11
        0.0000000000000002   12
        0.0000000000000001   13
        0.0000000000000005   14
        0.0000000000000001   15
        0.0000000000000004   16
        0.0000000000000001   17
        0.0000000000000008   18
        0.0000000000000000   19
        0.0000000000000008   20
        0.0000000000000000   21
        0.0000000000000006   22
        0.0000000000000000   23
        0.0000000000000013   24
        0.0000000000000000   25
        0.0000000000000009   26
        0.0000000000000000   27
        0.0000000000000011   28
        0.0000000000000000   29
        0.0000000000000012   30
        0.0000000000000000   31
        0.0000000033273433   32
        0.0000000000000000   33
        0.0000000291394506   34
        0.0000000000000000   35
 
INT_EXACTNESS_CHEBYSHEV1:
  Normal end of execution.
 
25 February 2008  12:07:00.452 PM