Currently, I am trying to figure out how to solve a non-linear system using a model. The model is:
m2(x) = a*x + 2*exp(b*x)
I have to solve for a and b using the data:
x = [0.00,0.25,0.50,0.75,1.00];
y = [2.10,3.70,6.26,10.03,16.31];
Using that I solve the following cost function:
(a,b) = sum(y(i) - m2(x(i))^2
I have been trying for a while now and I can't figure out how to extract a and b from m2(x(i)). fsolve has not worked for me, I have also tried the routine solve function. I am not looking for an answer but I am looking for a direction to take as I am at a complete roadblock.
Edit: The model captures the dependence of y on the independent variable x I ran this function to get the 5 equations.
function [f] = func(x,y)
syms a b
f = a*x + 2 * exp(b*x) == y;
end
With the driver:
for i = 1:5
f(i) = func(x(i),y(i));
end
disp(f');
your unknowns are a,b so I parametrized them as w in the model, instead of what you did. I used lsqnonlin and solved as follows:
x = [0.00,0.25,0.50,0.75,1.00];
y = [2.10,3.70,6.26,10.03,16.31];
m2 = @(w) w(1)*x + 2*exp(w(2)*x);
cost_func = @(w) m2(w)-y;
v = lsqnonlin(cost_func,[1 1]); % normal least squares
plot(x,y,'x',x,m2(v));