fsolve issue with high gradient function

Hello,

I am in front of an issue with fsolve, I have a function which varies very very quickly with at least 10 solutions where f(x) = 0

when I plot with log(1+f(x)) I can see where the solutions are :

for example for the sixth one it is 7.2* omg = 399 hz

I verified by plotting the function on the intertval 7.1 7.3 * omg and it cross 0 once (as you can see it is power 20)

So to find the root I tried to do

fre6 = @(x) det(f(x,xi,A,CAP,ns,ork))/10^21;

w6 = fsolve(fre1,7*omg)

fsolve return no solution even if :

• I change the initial guess
• I change 10^21 to decrease the gradient

any help will be amazing

I already read some topic such as

fsolve no solution found. - MATLAB Answers - MATLAB Central (mathworks.com)

but it does not work when I change the initial guess

Answer 1

[Matt J]

You should not be using fsolve for a 1D root finding problem, and particularly not when the function is highly non-differentiable. Just do a sweep,

x= linspace(0,9,100);

fvals=arrayfun(fre,x);

loc=find(abs(fvals)<=tolerance);

xroots=x(loc);

Now, if you wish to refine the root calculations, you can use xroots as starting points in calls to fzero.