Lecture 21
Polynomial interpolation with the Newton
basis
Today we looked at Newton divided differences. I
derived the divided difference for a degree two polynomial. 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.
I also showed how
Horner's rule can be used to evaluated the interpolating polynomial using the
coefficients of the Newton basis. The advantage of using Horner'r rule is
misstated in the Ellis notes. Ellis remarks that Horner's rule uses half the
number of multiplications when in fact it uses roughly the square root of the
number of multiplications.
Posted: Fri - October 29, 2004 at 12:58 PM