(a) Interpolate the function f (x) = sin(x) at 5 Chebyshev points over the interval [0,π/2]. Compare your results to those of Exercises 3 and 16.
(b) Repeat the interpolation, this time using 5 Chebyshev points over the interval [0,π]. Plot f (x) as well as the interpolant. What are your conclusions?
Exercises 3
Use the known values of the function sin(x) at x = 0,π/6,π/4,π/3 and π/2 to derive an interpolating polynomial p(x). What is the degree of your polynomial? What is the interpolation error magnitude |p(1.2)-sin(1.2)|?
Exercises 16
For the problem of Exercise 3, find an error bound for the polynomial interpolation on [0,π/2]. Compare your error bound to the actual interpolation error at x = 1.2.