|Re: Numerical Integration|
Message #7 Posted by Allen on 22 Nov 2011, 9:57 p.m.,
in response to message #1 by Namir
I wonder if you have considered using something other than the monomial basis for your objective function for your numeric integration??
For example, whether using uniform weighting or individual weights, you can use the method of undetermined coefficients to solve the abscissa locations. For example to find a three point, equal-weighted solution on the following range:
With 4 unknowns, you can just use this equation:
to find +/-inv(sqrt(2)), and 0 are the nodes, with the weight w=2/3.
Any number of weights or points can be calculated this way, but this only uses the monomial basis. With a different (perhaps higher-order?) basis function, Could it be more accurate??
Edited: 22 Nov 2011, 10:07 p.m.