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_modified_x.txt".
  Quadrature rule W file = "gen_lag_o16_a0.5_modified_w.txt".
  Quadrature rule R file = "gen_lag_o16_a0.5_modified_r.txt".
  Maximum degree to check = 35
  Weighting exponent ALPHA = 0.5
  OPTION = 1, integrate                 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

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

  Weights W:

  w[ 0] =       0.2950148257926292
  w[ 1] =       0.5926504061509453
  w[ 2] =       0.8956575998744516
  w[ 3] =        1.207063433953284
  w[ 4] =        1.530352787791976
  w[ 5] =        1.869714179339352
  w[ 6] =        2.230395748423061
  w[ 7] =        2.619252244761896
  w[ 8] =        3.045634801992271
  w[ 9] =         3.52292968201735
  w[10] =        4.071417057880741
  w[11] =        4.724080738693911
  w[12] =        5.539909876059123
  w[13] =        6.639993574123777
  w[14] =        8.335658835078922
  w[15] =        11.89633502881635

  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
     8.351683545445299e-16   1
     1.202642430544123e-15   2
     6.108659964668561e-16   3
     1.357479992148569e-16   4
       1.9745163522161e-16   5
     1.215086985979139e-16   6
                         0   7
     1.219852032982979e-16   8
                         0   9
     1.565323911998208e-16  10
     2.395626160971164e-15  11
     8.362913143753911e-16  12
     4.625413689384855e-15  13
     4.192493196289756e-15  14
     3.386922974842773e-15  15
     1.277223478728582e-15  16
     2.835957438483067e-15  17
     3.462663454300472e-15  18
     9.470532524582465e-16  19
     5.358935477324679e-15  20
     3.162932246440234e-15  21
     3.911645676757019e-16  22
     8.921881203156351e-15  23
     3.304601749326304e-15  24
     5.019993575859987e-15  25
     2.767379559456837e-15  26
     1.686783731478461e-15  27
     2.926986762118911e-15  28
     7.844207793196006e-15  29
     5.682611110137386e-15  30
     2.985936872321772e-15  31
     1.189840681881813e-09  32
     1.994308862397206e-08  33
     1.720073246770339e-07  34
     1.017043578067322e-06  35

INT_EXACTNESS_GEN_LAGUERRE:
  Normal end of execution.

03 February 2008 11:43:48 AM