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