Lecture 25.
Gaussian
Quadrature
Today we looked
at Gaussian quadrature. I went over the two node case. I showed how solving a
system of 4 non-linear equations one could obtain c1,c2, x1, x2, such that the
value of the integral in an interval -1..1, could be obtained by the weighted
sum c1*f(x1) + c2*f(x2). The value of the integral is exact for polynomials up
to degree 3 and an approximation for arbitrary functions. I then showed how one
can use a change of variable so that Gaussian quadrature can be applied to
integrals over any interval a..b.
Posted: Mon - November 6, 2006 at 07:18 AM