I have to solve un overdetermined system with least squares method. I wrote in matlab 'A\b' and it gives me only one solution correct. Why? Or how can I solve the problem efficently?

up-Xup*up-Xuu*u^2-Xvv*r^2-Xvr*v*r-v*r-Xrr*r^2 = 2*Xr+2*Xp

This is my equation. I have to find Xup, Xuu, Xvv, Xvr, Xrr. For solving this I have a folder .xlsx from where I import some values for coeff. of my unkowns.

In fact, this means I define my matrix (A and b).

To solve this I wrote A\b in matlab but the answer is not as I expected.

I must use least squares method.

Thaanks!

[Torsten]

A\b uses least squares method if the system is overdetermined.

[Paul-Catalin Puscasu]

If I solve mathematically for example M = At*A, N = At*B, where At = transpose(A) and than x = M\N it gives me a warning. : 'Matrix is singular to working precision.' And if I solve x = A\b it gives me a warning about rank.

[Paul-Catalin Puscasu]

and all solutions is NaN.

Answer 1

[John D'Errico]

help pinv

help lsqminnorm

Either will apply.