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_o2_a0.5_x.txt".
Quadrature rule W file = "gen_lag_o2_a0.5_w.txt".
Quadrature rule R file = "gen_lag_o2_a0.5_r.txt".
Maximum degree to check = 5
Weighting exponent ALPHA = 0.5
OPTION = 0, integrate x^alpha*exp(-x)*f(x)
Spatial dimension = 1
Number of points = 2
The quadrature rule to be tested is
a generalized Gauss-Laguerre rule
ORDER = 2
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] = 0.7233630235462755
w[ 1] = 0.1628639019064825
Abscissas X:
x[ 0] = 0.9188611699158102
x[ 1] = 4.08113883008419
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 = 3
Error Degree
1.252752531816795e-16 0
1.67033670908906e-16 1
1.336269367271248e-16 2
1.52716499116714e-16 3
0.126984126984127 4
0.3578643578643578 5
INT_EXACTNESS_GEN_LAGUERRE:
Normal end of execution.
03 February 2008 11:43:48 AM