Finding the multiple zeros within a prescribed interval

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Matthew Hunt 2018-11-13

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评论： Torsten 2018-11-14

I wish to solve the nonlinar function:

within a prescribed interval, say (0,100] say, I'm aware of using an annonymous function and using fzero or fsolve, but how do I get say multiple solutions?

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Torsten 2018-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/429607-finding-the-multiple-zeros-within-a-prescribed-interval#answer_346715

编辑：Torsten 2018-11-13

deltax = 1e-4;
xright = 100;
n = floor(xright/pi);
fun = @(x)tan(x)-x;
for i=1:n
  left = (2*i-1)*pi/2.0 + deltax;
  right = (2*i+1)*pi/2.0 - deltax;    
  sol(i) = fzero(fun,[left right]);
end
sol
fun(sol)

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Matt J 2018-11-13

编辑：Matt J 2018-11-13

No, the strategy to find all zeros of a function in a specified interval will always depend on the behaviour of the function itself. So no general guideline can be given.

Imagine, for example, that you were instead trying to find all roots of

contained in the interval [0,a]. No matter what

you choose, there would always be infinite roots in the interval.

Torsten 2018-11-14

@Matthew Hunt:

You know that tan(x) -x -> -Inf for x->2*(k-1)*pi/2 from the right and tan(x) - x -> +Inf for x->2*(k+1)*pi/2 from the left. So there must be a root in the interval 2*(k-1)*pi/2 : 2*(k+1)*pi/2. Plotting the function tan(x) - x you can see that there is exactly one root in this interval. This explains my code and the fact that it captures all roots in a specified interval.

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