# Solving for coefficients in polynomial

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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.

##### 0 Comments

### Answers (2)

Matt J
on 4 Apr 2019

Edited: Matt J
on 4 Apr 2019

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

x=M\z;

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.

##### 2 Comments

Matt J
on 4 Apr 2019

if you are assuming that A8, A9, A11-A21 are all zero, then yes, what you say is correct.

Walter Roberson
on 3 Apr 2019

k = 4:7;

A45 = [k .* A(k) .* (eta./eta_c).^k]\(Z_MD - Zfixed); % Solve for the higher order coefficients. This is the norm solution.

and you could also use k = [4:7, 10]

##### 5 Comments

Benjamin Cowen
on 4 Apr 2019

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