03 February 2008 11:43:48 AM

INT_EXACTNESS_GEN_LAGUERRE
  C++ 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_o16_a0.5_x.txt".
  Quadrature rule W file = "gen_lag_o16_a0.5_w.txt".
  Quadrature rule R file = "gen_lag_o16_a0.5_r.txt".
  Maximum degree to check = 35
  Weighting exponent ALPHA = 0.5
  OPTION = 0, integrate x^alpha*exp(-x)*f(x)

  Spatial dimension = 1
  Number of points  = 16

  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER = 16
  with A =     0
  and  ALPHA = 0.5

  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[ 0] =      0.09774098913713274
  w[ 1] =       0.2523079012122731
  w[ 2] =       0.2724198251520776
  w[ 3] =       0.1716635071262904
  w[ 4] =      0.06954026102655395
  w[ 5] =      0.01873480877845603
  w[ 6] =     0.003381229238954949
  w[ 7] =    0.0004052556900801655
  w[ 8] =    3.156131814886896e-05
  w[ 9] =    1.541304259364148e-06
  w[10] =    4.474937802762097e-08
  w[11] =      7.1360371637516e-10
  w[12] =    5.532849784136906e-12
  w[13] =    1.703727514691121e-14
  w[14] =    1.418249588844851e-17
  w[15] =    1.213712303922958e-21

  Abscissas X:

  x[ 0] =        0.147399184616311
  x[ 1] =       0.5909018112431889
  x[ 2] =        1.334487511614577
  x[ 3] =        2.385011552004654
  x[ 4] =        3.752567873874769
  x[ 5] =        5.451062939568397
  x[ 6] =        7.499085532907372
  x[ 7] =         9.92121913607243
  x[ 8] =        12.75005546011707
  x[ 9] =        16.02938636037513
  x[10] =        19.81951287710202
  x[11] =        24.20668064346831
  x[12] =        29.32145610335233
  x[13] =        35.37955078717556
  x[14] =        42.79325597075464
  x[15] =        52.61836625575324

  Region R:

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

  A generalized Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree = 31

          Error          Degree

     6.263762659083974e-16   0
     1.169235696362342e-15   1
     1.336269367271248e-15   2
     7.635824955835701e-16   3
     4.072439976445707e-16   4
       1.9745163522161e-16   5
     1.215086985979139e-16   6
     5.184371140177659e-16   7
     7.319112197897872e-16   8
     8.217950537990593e-16   9
     1.565323911998208e-15  10
     4.355683929038481e-16  11
     2.787637714584637e-15  12
     2.477900190741886e-15  13
     6.015316325111389e-15  14
     4.892222074772895e-15  15
                         0  16
     3.836883593241797e-15  17
     4.039774030017218e-15  18
      1.42057987868737e-15  19
     5.174144598796241e-15  20
     3.162932246440234e-15  21
      5.86746851513553e-16  22
     8.921881203156351e-15  23
     3.130675341467025e-15  24
     4.583472395350422e-15  25
     3.030939517500346e-15  26
     1.073407829122657e-15  27
     3.443513837786954e-15  28
     8.591275202071817e-15  29
     4.506898466660685e-15  30
     2.189687039702633e-15  31
     1.189841465881648e-09  32
     1.994308956009127e-08  33
     1.720073255453184e-07  34
     1.017043578850001e-06  35

INT_EXACTNESS_GEN_LAGUERRE:
  Normal end of execution.

03 February 2008 11:43:48 AM