<f,g> := 1∫3f(t)g(t)dt, f,g E C[1,3].
Let f(t) = 1/t, t E [1,3].
(i). Show that the constant polynomial g which best approximates f on [1,3] (in the sense of least squares) is given by
g(t) = ½ ln3, t E [1,3].
Find the mean square deviation ||f-g||2.
(ii) Find the best linear polynomial approximate to f on [1,3] and calculate the corresponding mean square deviation.
(See attached file for full problem description and accurate equations)
Inner Product, Linear Space, Constant Polynomial and Mean Square Deivation are investigated. The solution is detailed and well presented.