How do I find all the zeros of a function?

The FZERO function only finds a single zero near a specified point. How can I get different zeros over a wider range?

Answer 1

[MathWorks Support Team]

The example below describes one way to find zeros between 0 and 2*pi.

lb = 0;             % Set a lower bound for the function.
ub = 2*pi;          % Set an upper bound for the function.
x = NaN*ones(100,1);             % Initializes x.
starting_points=linspace(0,2*pi,100);
for i=1:100
        % Look for the zeros in the function's current window.
        x(i)=fzero(@(x)sin(10*x), starting_points(i));
end
x_unique=x(diff(x)>1e-12)

%compare to theory values
transpose(((0:19)*pi)/10)-x_unique
Changing the step value of the loop (0.01) to a larger value will result in faster execution, but less accuracy, and vice versa when the specified step value is smaller.

The tolerance for duplicates, in this example 1e-12, should be specified depending on the problem at hand, an inappropriate setting for a certain problem might result in some of the zeros not being found.

Alternately, you can use the SOLVE function from the Symbolic Math Toolbox. 

[Walter Roberson]

Note: solve() from the Symbolic Math Toolbox will only return all zeros for polynomial functions, not for nonlinear functions.

[Walter Roberson]

@ismail ismail

Time = 2:.1:4;
Dirac3 = zeros(size(Time));
Dirac3(Time==3) = 1;
stem(Time, Dirac3)