Multiple linear system, same solution

Question

I know how to solve the problem

Ax=B

with matlab, I just use mldivide to obtain x: x=A\B

But what if I have multiple basis A_i and multiple data B_i but the nature of the problem suggests me that the solution x must be the same for every i?

Answer 1

You could try stacking the A matrices and B vectors to obtain a larger least squares system. That is, form

A = (A_1)
    ...
    (A_n)

and

B = (B_1)
    ...
    (B_n)

and then solve

A*x = B 

in the least squares sense

The solution x to such a system will be the value that minimises

Sum{ || A_i*x - B_i ||^2 }