fzero function calculating all zeros within interval

Hello,

I was thinking about the function fzero. If you have a function that has multiple roots within an interval of your choice, is there a way to show all the roots as an array, instead of only one root closest to the guess?

Answer 1

[Star Strider]

You can first get an estimate of the zeros (if any) in your interval-of-interest by calculating it in that interval, then multiplying the function by circshift of the function to detect any zero-crossings that might be present. After that, use those estimates as your initial guesses for fzero

To illustrate:

x = linspace(0,50,200);
y = @(x) sin(x);
zx = x(y(x).*circshift(y(x),[0 -1]) <= 0);  % Estimate zero crossings
zx = zx(1:end-1);                           % Eliminate any due to ‘wrap-around’ effect
for k1 = 1:length(zx)
    fz(k1) = fzero(y, zx(k1));
end

[mostafa]

It should be corrected to this.

x = linspace(0,50,200);
y = @(x) sin(x);
zx = y(x).*circshift(y(x),[-1]) <= 0;  % Estimate zero crossings
zx = zx(1:end-1);                      % Eliminate any due to ‘wrap-around’ effect
zx = x(zx);
for k1 = 1:length(zx)
    fz(k1) = fzero(y, zx(k1));
end
fz

Answer 2

[Ben11]

If you have the Curve Fitting Toolbox you might want to use

fnzeros

Info here

Answer 3

[Matt J]

Not for general functions. Certain functions, for example, have infinite roots in a finite interval, e.g., f(x)=0 or f(x)=sin(1/x). So of course the routine won't find all of them for you.

You can't reliably find multiple roots without exploiting some specific apriori known thing about the structure of the function, e.g., that it's a polynomial.