lsqnonlin function take two initial guess for two different matrix parameter

I was working on a project trying to use Levenberg Marquardt algorithm to find suitable F and P result that will minimize:

    F(i = 1 to 10) = sum( u(i) - F*P )

In this equation, F is a 3X4 matrix and P is a 4X3 matrix.

I know lsqnonlin() function can take one initial guess, so I can initial an F with zeros and pass to the lsqnonlin to get the solution for F. However, I think I will need to pass both F and P with an initial guess and find the solution for both.

Is there a way we can pass two initial guesses into lsqnonlin, or I need to combine P and F into one, however, they have different dimensions.

Answer 1

[Walter Roberson]

You have F on both sides of the equation.

On the right side it appears to be 3 x 4 and P is 4 x 3 so F*P is 3 x 3 and u(i) - F*P would be 3 x 3, and sum() of that would then be 1 x 3.

The left side must have the same size as the right, so F(i) must be 1 x 3. We see from the "i = 1 to 10" that there must be at least 10 such F(i), which gives at least 10 * (1 x 3) = 30 values. But the right hand side F is only 12 values.

At this point we are stuck and must guess that the problem has not been correctly defined.