CODEWITHSUNDEEP
functionmatlab
Michael
Michael

Reputation: 644

(Easy) Matlab: finding zero spots (fzero)

I'm all new to Matlab and I'm supposed to use this function to find all 3 zero spots.

f.m (my file where the function can be found)

function fval = f(x)
% FVAL = F(X), compute the value of a test function in x
fval = exp(-x) - exp(-2*x) + 0.05*x - 0.25;

So obviously I write "type f" to read my function but then I try to do like fzero ('f', 0) and I get the ans 0.4347 and I assume that's 1 of my 3 zero spots but how to find the other 2?

Upvotes: 1

Views: 9945

Answers (2)

Rody Oldenhuis
Rody Oldenhuis

Reputation: 38032

Just to complement Gunther Struyf's answer: there's a nice function on the file exchange by Stephen Morris called FindRealRoots. This function finds an approximation to all roots of any function on any interval.

It works by approximating the function with a Chebyshev polynomial, and then compute the roots of that polynomial. This obviously only works well with continuous, smooth and otherwise well-behaved functions, but the function you give seems to have those qualities.

You would use this something like so: 

%# find approximate roots
R = FindRealRoots(@f, -1, 10, 100);

%# refine all roots thus found
for ii = 1:numel(R)
    R(ii) = fzero(@f, R(ii)); end

Upvotes: 0

Gunther Struyf
Gunther Struyf

Reputation: 11168

From fzero documentation

x = fzero(fun,x0) tries to find a zero of fun near x0, if x0 is a scalar. fun is a function handle. The value x returned by fzero is near a point where fun changes sign, or NaN if the search fails. In this case, the search terminates when the search interval is expanded until an Inf, NaN, or complex value is found.

So it can't find all zeros by itself, only one! Which one depends on your inputted x0.

Here's an example of how to find some more zeros, if you know the interval. However it just repeatedly calls fzero for different points in the interval (and then still can miss a zero if your discretization is to coarse), a more clever technique will obviously be faster:

http://www.mathworks.nl/support/solutions/en/data/1-19BT9/index.html?product=ML&solution=1-19BT9

As you can see in the documentation and the example above, the proper way for calling fzero is with a function handle (@fun), so in your case:

zero1 = fzero(@f, 0);

From this info you can also see that the actual roots are at 0.434738, 1.47755 and 4.84368. So if you call fzero with 0.4, 1.5 and 4.8 you probably get those values out of it (convergence of fzero depends on which algorithm it uses and what function you feed it).

Upvotes: 2

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