Lecture 17.
Polynomial Interpolation with the Lagrange
basis.
Today we saw that we can use
the Lagrange basis for polynomial interpolation. The Lagrange basis is not
likely to cause numerical errors as is the case when using the monomial basis
for polynomial interpolation.
Polynomial interpolation with
the Newton basis
Today we looked at
Newton divided differences. I wrote out the divided difference for a degree two
polynomial, but I did not derive it on the board. Please note the derivation in
Recktenwald leads to a formulation that does not match the usual divided
difference form. There is also an error in the way f[x1,x2,x3] is defined on
page 540. If you follow the derivation the first term in the numerator should be
f[x1,x3]. This error is reported in the errata updates on the NMM web site.
Posted: Wed - October 18, 2006 at 01:50 PM