Lecture 26
Composite quadrature.
The lecture today began with some
demonstrations using Matlab. I ran Recktenwald's plotTrapInt and
plotSimpInt on the 'humps' function,
in the interval 0..1. This illustrated the technique of breaking up an interval
into panels and applying an integration rule to each panel. This is called
composite quadrature. I then used Moler's quadgui to perfomr the same
integration but using an adaptive Simpson's method.
Adaptive quadrature is a
technique that automatically determines how many panels to use (and where to put
them) so that a numerical integral is computed within the prescribed accuracy.
We saw how the rounding error could be estimated, and how this estimate is used
in a recursive adaptive trapezoid rule as well as a recursive adaptive Simpson's
rule algorithm.
Tomorrow's
class is cancelled (as are all Queen's classes at 10:30 -11:30) so that you may
attend Remembrance Day ceremonies.
Posted: Thu - November 10, 2005 at 12:04 PM