How to find zeros of a function?

For instance,

x = -3.55:0.1:3.55;

y = x.^2 - 4;

Obviously, when x=2 or -2, y=0.

But I want to know how to use matlab to find zeros of a function y = f(x) when x is a matrix defined by the user like the above case.

[Wenjie]

I want to use fzero to do so, but I don't know how, since x is a matrix, rather than a symbolic function.

[Mark Sherstan]

As per documentaiton note:

x = fzero(fun,x0) tries to find a point x where fun(x) = 0. This solution is where fun(x) changes sign—fzero cannot find a root of a function such as x^2.

[Akira Agata]

If your function is always polynomial, you can use roots function to do this task. Please look at the following help page.

https://www.mathworks.com/help/matlab/ref/roots.html

Answer 1

[Alexander]

If it's not a function but meassured data I would go like this in a first try:

x = -3.55:0.0001:3.55; % assuming 10 kHz sample frequency
y = x.^2 - 4;
yS = sign(y);
dyS = diff(yS);
Z=find(dyS ~= 0);
x(Z)

[DAVID]

This was really elegant, thanks!

Answer 2

[Wenjie]

I've found the solution. First, define the function in a separate file as

function y = fun(x)
y = x.^2-4;
end

Then use fzero to find x value that will give y=0.

x0 = fzero(@(x) fun(x), 3)

[Walter Roberson]

However this is not suitable for the case where x is a matrix like you asked in your Question.

fzero() itself is also not suitable for the case where you have an array-valued (probably multivariate) function: you need fsolve() from the Optimization Toolbox for that.

[Nico]

What does the @(x) and the 3 mean? Sorry I'm university student with no experience...

[Dyuman Joshi]

@(x) is the syntax used to define a Function Handle / Anonymous Functions

The 3 is provided as an initial guess for fzero() to work with - see fzero for more information.

Answer 3

[Walter Roberson]

x(y==0)

Note that this can miss an indefinite number of zeroes of a function if the x do not happen to sample at the right places . It also will not detect zero crossings between x values . You could make use of the results to get hints about zero crossings .