22 March 2020 07:31:54 PM
LAGUERRE_EXACTNESS
C++ version
Compiled on Mar 22 2020 at 19:28:43.
Investigate the polynomial exactness of a 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.
The quadrature file rootname is "lag_o04".
The requested maximum monomial degree is = 10
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 = 10
OPTION = 0, integrate exp(-x)*f(x)
Spatial dimension = 1
Number of points = 4
The quadrature rule to be tested is
a Gauss-Laguerre rule
ORDER = 4
with A = 0
Standard rule:
Integral ( A <= x < +oo ) exp(-x) f(x) dx
is to be approximated by
sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
Weights W:
w[ 0] = 0.6031541043416337
w[ 1] = 0.3574186924377999
w[ 2] = 0.03888790851500538
w[ 3] = 0.0005392947055613278
Abscissas X:
x[ 0] = 0.3225476896193923
x[ 1] = 1.745761101158346
x[ 2] = 4.536620296921128
x[ 3] = 9.395070912301136
Region R:
r[ 0] = 0
r[ 1] = 1e+30
A Gauss-Laguerre rule would be able to exactly
integrate monomials up to and including degree = 7
Error Degree
2.220446049250313e-16 0
2.220446049250313e-16 1
0 2
1.480297366166875e-16 3
1.480297366166875e-16 4
7.105427357601002e-16 5
1.263187085795734e-15 6
2.165463575649829e-15 7
0.0142857142857114 8
0.06507936507936186 9
0.1641269841269807 10
LAGUERRE_EXACTNESS:
Normal end of execution.
22 March 2020 07:31:54 PM