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