How to calculate Matrix A?! (Fitting or ...)

Hello everyone,

I need to calculate Matrix A, as you can see in the photo I have attached. (my system is a lot bigger, I simplified it in several rows and columns so it can be understood easily)

I know it can be done by Fitting, however, I do not know how I can define matrix A for this purpose. In Fitting, we can define xdata=F2 and ydata=F1; but what about A?!

If also, you know any other method to calculate A, please let me know.

Thanks, Peyman

[Danilo NASCIMENTO]

let me know first, you dont wanna type in the 49 elements of matrix A?

[Peyman]

Thanks for the reply and specially for comments and suggestions.

- No, I don't want to type in all elements. They need to be calculated (and used later in another place)

Answer 1

[John D'Errico]

You have a bi-diagonal matrix. One common trick is to use diag to create the main diagonal and then the sub-diagonal matrix, adding the two matrices together. Thus if a_main is a vector of main diagonal entries, and a_sub, the vector of the sub-diagonal entries...

a_main = rand(1,7);
a_sub = rand(1,6);
A = diag(a_main) + diag(a_sub,-1)A =
      0.75774            0            0            0            0            0            0
      0.27692      0.74313            0            0            0            0            0
            0     0.046171      0.39223            0            0            0            0
            0            0     0.097132      0.65548            0            0            0
            0            0            0      0.82346      0.17119            0            0
            0            0            0            0      0.69483      0.70605            0
            0            0            0            0            0       0.3171     0.031833

Better is to learn to use sparse matrices, here the appropriate function is spdiags, which will create the complete matrix in one call. The nice thing about a sparse matrix is the storage savings as well as a speed boost for large problems.

[Peyman]

- As I said, there is no limit to the matrix A; it changes with the system. And the aij also, are more than only two elements in each row, but the final matrix is still kind of a "lower triangular matrix".

- Did you just created two matrices with some numbers and then added them as matrix A? I get your point, but these aij arrays are coefficients in my equation and I want to find the coefficients.

- I can't have inverse matrix for F2(t) because it is not a square matrix! To find A, I need to use another approach. Do you have any opinion about this?