Explore BrainMass
Share

Fourier Series : Least-Squares Approximation and Mean Square Error

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

5. (a). Find the least squares approximation of sin(πx) over the interval [-1,1] by a polynomial of the form ao+ a1x+a2x².

(b). Find the mean square error of the approximation.

Note: Part (a) that is suppose to be sin(piex) and the polynomial is a sub 0, a sub 1, a sub 2. For some reason it wouldn't allow me to paste it in that format.

© BrainMass Inc. brainmass.com March 21, 2019, 12:29 pm ad1c9bdddf
https://brainmass.com/math/fourier-analysis/least-squares-approximation-mean-square-error-70454

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Problem:

(a). Find the least squares approximation of sin(πx) over the interval [-1,1] by a polynomial of the form ao+ a1x+a2x².

(b). Find the mean square error of the approximation.

Solution:

a) We need to minimize the integral:
...

Solution Summary

Fourier Series, Least-Squares Approximation and Mean Square Error are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19