Lecture 19.
Hermite
Interpolation
I
briefly went over the formulation of the equations used for Hermite
interpolation. This proved to be useful for
explaining:
Cubic
Splines
I worked
through a 4 knot example and we saw how to obtain 12 equations in 12 unknowns,
where the unknowns are the 4 coefficients for the three cubic curves. On the
first time through we saw the
fixed
slope end condition. In
general we need to solve a
4n by
4n
system of linear equations
to get the coefficients in
O(n3)
operations. We then saw how we could rearrange the equations and reduce the
computation to
O(n)
operations. Finally two more end conditions were discussed the
natural
and
not-a-knot
end conditions.
I
found a few minor typos in Recktenwald: Page 562 equation 10.35 it should be
Pi(⌃x).
Page
571 matrix 10.46
the
second
to
last
line
should
read 0
αn-1
ϐn-1
ϒn-1.
Posted: Mon - October 23, 2006 at 06:05 PM