20 January 2020 01:01:47 PM

LAGUERRE_EXACTNESS
  C version

  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] = 0.603154
  w[1] = 0.357419
  w[2] = 0.0388879
  w[3] = 0.000539295

  Abscissas X:

  x[0] = 0.322548
  x[1] = 1.74576
  x[2] = 4.53662
  x[3] = 9.39507

  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

     2.22045e-16   0
     2.22045e-16   1
               0   2
      1.4803e-16   3
      1.4803e-16   4
     7.10543e-16   5
     1.26319e-15   6
     2.16546e-15   7
       0.0142857   8
       0.0650794   9
        0.164127  10

LAGUERRE_EXACTNESS:
  Normal end of execution.

20 January 2020 01:01:47 PM