07-Jan-2022 22:44:17

laguerre_exactness_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test laguerre_exactness().
07-Jan-2022 22:44:17

LAGUERRE_EXACTNESS
  MATLAB version

  Investigate the exactness of a Gauss-Laguerre
  quadrature rule for integrating monomials
  with density exp(-x) or density 1
  over the [0,+oo) interval.

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 = 8
  OPTION = 0, integrate exp(-x)*f(x).

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Laguerre quadrature rule of ORDER = 4
  for integrals of the type:
    Integral ( 0 <= x < +oo ) f(x) exp(-x) dx

  Weights W:

  w(1) =       0.6031541043416337
  w(2) =       0.3574186924377999
  w(3) =       0.0388879085150054
  w(4) =       0.0005392947055613

  Abscissas X:

  x(1) =       0.3225476896193923
  x(2) =       1.7457611011583460
  x(3) =       4.5366202969211278
  x(4) =       9.3950709123011364

  Region R:

  r(1) = 0.000000e+00
  r(2) = 1.000000e+30

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

  Degree      Error

   0        0.0000000000000004
   1        0.0000000000000000
   2        0.0000000000000000
   3        0.0000000000000001
   4        0.0000000000000000
   5        0.0000000000000005
   6        0.0000000000000013
   7        0.0000000000000022
   8        0.0142857142857116

LAGUERRE_EXACTNESS:
  Normal end of execution.

07-Jan-2022 22:44:17

laguerre_exactness_test():
  Normal end of execution.

07-Jan-2022 22:44:17