This problem concerns a method to reduce the computational effort to evaluate the Lagrange interpolation function given in (5.5). (a) What is the flop count to evaluate (5.5) for a given value of ?...

This problem concerns a method to reduce the computational effort to evaluate the Lagrange interpolation function given in (5.5).

(a) What is the flop count to evaluate (5.5) for a given value of
?

(b) Assuming that


_i
, for any
, show that (5.5) can be written as

This is known as the first form of the barycentric interpolation formula, and


_i
’s are called barycentric weights.

(c) Suppose the formula in part (b) is used to interpolate the constant function
() = 1. Use this to show that

(d) Use the result from part (c) to show that

This is called the second (true) form of the barycentric formula.

(e) What is the flop count to evaluate the formula for


_n
() given in part (d)?