Looking for an iterative Solver to use in a loop with changing constants?

I have not used any kind of iterative solver but I am facing a challenge when trying to resolve the following equation:

sigma = theta+acos((A+B+(2*A*B/(2*A*B/(A+B-(B-A)*cos(2*theta))-(A+B))))/(B-A))/2;

A & B are variables input by the user but do not vary during the loop. Sigma is changing during the loop though and I need to determine theta at each loop. Can anyone advise an iterative solver to resolve this and demonstrate briefly how it would be used in this application since I have not used it before.

Thanks, Adam

[Sara]

doc fzero

Answer 1

[Star Strider]

This would be my approach:

thta = @(theta,sigma,A,B) sigma - (theta+acos((A+B+(2*A*B/(2*A*B/(A+B-(B-A)*cos(2*theta))-(A+B))))/(B-A))/2);
A = 3;
B = 5;
sgma = 0:7;
for k1 = 1:length(sgma)
    sigma = sgma(k1);    
    theta(k1) = fzero(@(theta) thta(theta,sigma,A,B),0);
end

The anonymous function thta is essentially your equation but subtracting it from sigma so it will have a root (zero) at theta. It will pick up A and B from the workspace and through the argument list, sigma will vary in the loop, and theta will be a vector containing one root (close to zero) for each set of arguments. If there are more than one root, you will need to provide initial estimates close to those roots.