Fitting least square approximations

[Gameowner]

Homework Statement

Attached

Homework Equations

The Attempt at a Solution

Thanks in advance for the help.

The problem I'm having is not so much as to how to solve the problem, but how to proceed using MATLAB. I'm having trouble figuring out how to enter in the respective components of this question into MATLAB.

The method I will try to solve this is by normal equations. To do this, I have to at least first specify what my A, b and x matrix/vectors are.

From here, I had that A is a matrix given by

A = [1 t1^2 t2^3 t3^4]
[1 t1^2 t2^3 t3^4]
[etc ]

and x is given by

x = [x1]
[x2]
[x3]
[x4]

b is given by

b = [phi(1)]
[phi(2)]
[phi(3)]
[phi(4)]

So my question is, how do I define these into matrix form without having actual numerical data points? We've only been shown how to approximate using normal equations/QR factorization, but with numerical data points, hence we could define the matrices.

I had to begin with

t = -1:0.1:1
A = [t.^0 , t.^1, t.^2, t.^3]

then after entering in the matrices, would then proceed to using backslash to solve hence plotting the approximation?

Any help, hint would be much appreciated.

 

[TheoMcCloskey]

Gameowner - lookup the topic "Continuous Least Squares". This addresses the problem that you have. And yes, constructing the Normal equations is correct approach, only you need to do it on the continuous domain.

One other suggestion; since your domain interval is symmetric about origin, consider re-ordering the basis functions into groups of even functions, followed by odd functions. Once you do that, this problem reduces to 2 simple manual excercises.