Linear Least Squares: Critical Points & Quadratic Polynomials

[sam.pat]

I have a question about Linear least squares:

In Linear least squares, For any critical point "x" it must follow the linear system:
A(Transpose) * Ax = b * A(Transpose) where x is the critical point.

But here x is an n vector, so does that mean there are as many critical points (x) as there are columns?

So in case of an quadratic polynomial : 1 + X2*t + X3*t^2 with three parameters, would we have three critical points?

|1 t1 t1^2 |
|1 t2 t2^2 |
|1 t3 t3^3 |
|1 ... ... |
|1 ... ... |

Thanks in advance

 

[lippyka]

!Yes, in the case of a quadratic polynomial with three parameters, there would be three critical points. The linear system A(Transpose) * Ax = b * A(Transpose) can be solved to find the values of x that are the critical points.