Cmpe 360

HW 8

Q1: Find the least squares polynomials of degrees 1, 2, and 3 for the data in the following table. Compute the error E in each case. Graph the data and the polynomials.

x_i 1.0 1.1 1.3 1.5 1.9 2.1

y_i 1.84 1.96 2.21 2.45 2.94 3.18

Solve the following three questions for the function f(x) = e^x

Q2: Find the linear least squares polynomial approximation on the interval [-1, 1].

Q3: Find the linear least squares polynomial approximation of degree 2 on this interval.

Q4: Compute the error E for Q2.

Q5: Find the general continuous least squares trigonometric polynomial S_n(x) for f(x), where

f(x) = 0, if –π < x ≤ 0

f(x) = 1, if 0 < x < π