MATLAB: How to use fzero and choose correctly initial guess

fzero with initial guess

Hi,

May I know how to solve the following equation with fzero and get two numbers: -2 and +2.

When I used the following code, it returned x=-2

fzero(@(x) x^2-4,0)

And this returned x=+2

fzero(@(x) x^2-4,1)

And furthermore, how can I choose correctly the initial guess number? I found that the answer will depend on the initial guess.

Best Answer

Whenever I have a function I want to use fzero with, I plot it to see how many zeros it has and about where they are. I then choose my initial estimates based on that.

A more mathematically correct approach involves taking the vector you want the zeros of, then multiplying it by a one-position circularly-shifted version of itself, using the circshift function. This produces negatives at the zero crossings that are easy to test for and determine the indices of using the find function. I then use the x-values at those indices as the initial estimates. The initial estimates don’t have to be perfect, just close enough. If there are several zero-crossings, you will get several answers from fzero. It is up to you to choose the ‘correct’ zeros.

Related Solutions

MATLAB: Fzero function calculating all zeros within interval

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

MATLAB: How do i find roots for a trignometric function? eg (0.1x)+10tan(0.1*x)

Use the fzero function to get real roots. Plot it first, since it likely has several, and the initial estimate of the roots will reveal different values:

eqn = @(x) (0.1*x)+10*tan(0.1*x);
rt = fzero(eqn, 10)
rt =
    15.7080

Best Answer

Related Solutions

MATLAB: Fzero function calculating all zeros within interval

MATLAB: How do i find roots for a trignometric function? eg (0.1*x)+10*tan(0.1*x)

Related Question

MATLAB: How do i find roots for a trignometric function? eg (0.1x)+10tan(0.1*x)