03-Feb-2008 11:49:34

INT_EXACTNESS_GEN_LAGUERRE
  MATLAB version

  Investigate the polynomial exactness of a generalized 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.

INT_EXACTNESS_GEN_LAGUERRE: User input:
  Quadrature rule X file = "gen_lag_o4_a0.5_x.txt".
  Quadrature rule W file = "gen_lag_o4_a0.5_w.txt".
  Quadrature rule R file = "gen_lag_o4_a0.5_r.txt".
  Maximum degree to check = 10
  Weighting function exponent ALPHA = 0.500000
  OPTION = 0, integrate x^alpha*exp(-x)*f(x).

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER = 4
  A =     0.000000
  ALPHA = 0.500000

  OPTION = 0, standard rule:
    Integral ( A <= x < oo ) x^alpha exp(-x) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

  w(1) =       0.4530087465586076
  w(2) =       0.3816169601717996
  w(3) =       0.0507946275722408
  w(4) =       0.0008065911501100

  Abscissas X:

  x(1) =       0.5235260767382691
  x(2) =       2.1566487632690938
  x(3) =       5.1373875461767113
  x(4) =      10.1824376138159192

  Region R:

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

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

      Error    Degree

        0.0000000000000000    0
        0.0000000000000003    1
        0.0000000000000003    2
        0.0000000000000005    3
        0.0000000000000005    4
        0.0000000000000008    5
        0.0000000000000016    6
        0.0000000000000023    7
        0.0105306458247667    8
        0.0504362510554501    9
        0.1330978618904358   10

INT_EXACTNESS_GEN_LAGUERRE:
  Normal end of execution.

03-Feb-2008 11:49:35