22 March 2020 07:31:54 PM

LAGUERRE_EXACTNESS
  C++ version

  Compiled on Mar 22 2020 at 19:28:43.

  Investigate the polynomial exactness of a Gauss-Laguerre
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the [0,+oo) interval.

  The rule may be defined on another interval, [A,+oo)
  in which case it is adjusted to the [0,+oo) interval.

  The quadrature file rootname is "lag_o04".

  The requested maximum monomial degree is = 10

LAGUERRE_EXACTNESS: User input:
  Quadrature rule X file = "lag_o04_x.txt".
  Quadrature rule W file = "lag_o04_w.txt".
  Quadrature rule R file = "lag_o04_r.txt".
  Maximum degree to check = 10
  OPTION = 0, integrate exp(-x)*f(x)

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Laguerre rule
  ORDER = 4
  with A = 0

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

  Weights W:

  w[ 0] =       0.6031541043416337
  w[ 1] =       0.3574186924377999
  w[ 2] =      0.03888790851500538
  w[ 3] =    0.0005392947055613278

  Abscissas X:

  x[ 0] =       0.3225476896193923
  x[ 1] =        1.745761101158346
  x[ 2] =        4.536620296921128
  x[ 3] =        9.395070912301136

  Region R:

  r[ 0] =                        0
  r[ 1] =                    1e+30

  A Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree = 7

          Error          Degree

     2.220446049250313e-16   0
     2.220446049250313e-16   1
                         0   2
     1.480297366166875e-16   3
     1.480297366166875e-16   4
     7.105427357601002e-16   5
     1.263187085795734e-15   6
     2.165463575649829e-15   7
        0.0142857142857114   8
       0.06507936507936186   9
        0.1641269841269807  10

LAGUERRE_EXACTNESS:
  Normal end of execution.

22 March 2020 07:31:54 PM