This problem concerns interpolating the function () = sin over the interval 1 ≤ ≤ 3, using three data points, with 1 = 1, 2 = 2, and 3 = 3. (a) Find the global interpolation polynomial that fits...

This problem concerns interpolating the function
() = sin

over the interval 1 ≤

≤ 3, using three data points, with

₁
= 1,

₂
= 2, and

₃
= 3.

(a) Find the global interpolation polynomial that fits this data.

(b) Find the piecewise linear interpolation function that fits this data.

(c) Find the natural cubic spline that fits this data.

(d) Find the clamped cubic spline that fits this data.

(e) Chebyshev interpolation cannot use the stated


_i
’s. What are the three Chebyshev interpolation points for this interval, and what is the resulting interpolation function?