I have the following equation in MATLAB which solves for my coefficients:
A45 = [(eta./eta_c).^(4:7).*(4:7)]\(Z_MD - Zfixed); % Solve for the higher order coefficients. This is the norm solution.
This represents the summation part of this equation:
I set the first 3 coefficients which is why it just goes from 4 to 7.
As you can see, since the equation is a sum over k*A_k*(eta./eta_c)^k. I believe the above equation solves for each A_k, correct? i think it does, but I'm not sure how it does it. The A_k's are not even in the MATLAB equation. How does it know to create these coeffs and solve for them?
Also, what if I wanted to have order 4-7 polynomial, but then I wanted to skip 8 and 9 and do 10? How would I do that?
The following does not work:
A45 = [(eta./eta_c).^(4:7,10).*(4:7,10)]\(Z_MD - Zfixed); % Solve for the higher order coefficients. This is the norm solution.
How does it know to create these coeffs and solve for them?
In Matlab, if you have a matrix equation M*x=z, you can solve for x by doing
In the special case where M is a square non-singular matrix, this is similar to doing x=inv(M)*z, but better. This is all that the code you've posted is doing, for a particular choice of the matrix M and z.
How does it know how many x(i) to solve for? From the number of columns of the matrix M.