Lecture 16.
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. However, it is more expensive to do polynomial evaluation with
the Lagrange basis, O(n2) versus O(n) when using the monomial basis
and the nested evaluation algorithm (Horner's method). You can find material on
the Lagrange basis in Recktenwald section 10.2.2, and in the Ellis notes class
10.
Please note: Rec Chapter 8
Question 30 of HW-6 has a error. It should say that K_1(D) = 1. Bonus, which
diagonal matrix has condition number alpha^2?
Posted: Tue - October 18, 2005 at 12:04 PM