Hi SungMin,
I understand that you want to solve the following system of equations using the Levenberg-Marquardt method in MATLAB, but the results for 𝑋(1) and 𝑋(2) are not as expected.
Here's a revised approach to ensure you correctly use the fsolve function with the Levenberg-Marquardt algorithm:
% Define the function
F = @(X) [d(1,3)*(abs(X(1)/(X(2)^2*ar))+d(2,3)*(X(1)/(X(2)^2*ar)))^d(3,3)*(bg_loc_M)+d(4,3)*(X(2))^d(5,3)-l/X(2);
abs(c(1,3))*(bg_loc_M)^c(2,3)*X(2)^c(3,3)*(ar)^c(4,3)*exp(-abs(c(5,3))*abs(X(1)+c(6,3)*abs(X(1)))^abs(c(7,3)))-foc];
% Initial guess
x0 = [0, l];
% Set options for fsolve
opts = optimoptions('fsolve', 'Algorithm', 'levenberg-marquardt', 'TolX', 1e-10, 'Display', 'iter');
% Solve the system of equations
[X, fval, exitflag, output] = fsolve(F, x0, opts);
% Display the results
disp(['X(1) = ', num2str(X(1))]);
disp(['X(2) = ', num2str(X(2))]);
% Check the output status
if exitflag <= 0
disp('The solver did not converge to a solution.');
else
disp('The solver converged to a solution.');
end
Ensure that the initial guess x0 is close to the expected solution and that all parameters (d, ar, bg_loc_M, l, c, foc) are correctly defined.
You can refer to the MathWorks documentation for more details on fsolve and its options: https://www.mathworks.com/help/optim/ug/fsolve.html
Hope this helps.
Regards,
Nipun
