Given a data set ( 1 , 1 ), ( 2 , 2 ), ··· , ( 101 , 101 ) suppose one of the following interpolation methods is to be used: Lagrange interpolation, piecewise linear interpolation, cubic spline...

Given a data set (
₁,

₁), (
₂,

₂), ··· , (
₁₀₁,

₁₀₁) suppose one of the following interpolation methods is to be used: Lagrange interpolation, piecewise linear interpolation, cubic spline interpolation using cubic B-splines.

(a) Order them by the number of flops needed to determine the interpolation function. Make sure to explain how you arrive at your answer. Assume the Thomas algorithm is used for the cubic spline (see Section 3.8).

(b) Order the methods by the number of flops needed to evaluate them at a given point (assume this point isn’t in the data set). Make sure to explain how you arrive at your answer.