Iterative solution of non-linear equation with a provided guess value?

I am looking for a solution to the problem:

ag_p*Gamma_p - Sa = 0 with Gamma_p = A+B*ag_p.

A, B and Sa are constants.

This can be solved by performing iterations starting with a certain guess value for ag_p.

Note: I have solved it through FZERO function as given below. I am interested to iteratively solve the equation by assigning a guess value to ag_p, let's say from [0...inf], which updates Gamma_p and the iterations are performed until the solution is found ( Something similar to Solve Block in MathCAD). I need to have a numerical value for Gamma_p in each iteration because I will be comparing its value with another constant parameter to define some "if" conditions.

Sa = 2.7956;
A = 2.24;
B = 0.5547;
Gamma_p = @(ag_p) A+B*ag_p;
f = @(ag_p) ag_p*Gamma_p(ag_p) - Sa;
z = fzero(@(ag_p) f(ag_p), 1E-3)

Thank you,

Answer 1

[Matt J]

Using fsolve() instead of fzero(), you could solve the problem as a system of two equations in two unknowns. The two unknowns are [ag_p, Gamma_p] and the two equations are,

 ag_p*Gamma_p - Sa    = 0 
 B*ag_p + A - Gamma_p = 0 

Answer 2

[Matt J]

You could use fzero's OutputFcn option

https://www.mathworks.com/help/optim/ug/fzero.html#btn3z5s-options

to access the sequence of ag_p iterates. It is then a simple matter to generate the corresponding sequence of Gamma_p values using the equation Gamma_p = A+B*ag_p.