find roots through iterative method
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I need to find 3 roots of an equation (e^x=3*x^2 - transcendent equation) through the iteration method in Matlab. What algorithm should I use?
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Accepted Answer
Matt J
on 5 Apr 2015
Edited: Matt J
on 5 Apr 2015
You can use FZERO, e.g.,
>> f=@(x) exp(x)-3*x.^2
>> [xroot,res]=fzero(f,.1)
You will need to provide an initial guess of each of the three roots, which you can obtain by plotting the function f(x)=e^x-3*x^2
10 Comments
James Tursa
on 8 Apr 2015
Edited: James Tursa
on 8 Apr 2015
f = @(x) 3*x.^2-exp(x)
x = -5:.01:5;
plot(x,f(x))
grid on
All three roots are on the plot.
More Answers (1)
paula ro
on 8 Apr 2015
2 Comments
James Tursa
on 8 Apr 2015
Sounds like you are asking quite a lot from this algorithm. Determining good starting guesses for an arbitrary function is not at all trivial. Even determining just how many roots there are is not trivial. You are certainly not going to get some simple code on this forum that does this for you for an arbitrary function. Seems like there is going to have to be some manual work from you up front for doing this for any particular function you are interested in.
Matt J
on 9 Apr 2015
Edited: Matt J
on 9 Apr 2015
But I need an iteration algorithm that finds these 3 roots without me manually extracting the intervals from the plot.
You've wasted a lot of time by concealing that requirement. I advised you to find the 3 roots in this manual way in my very first response and in several subsequent comments. You didn't even blink.
As James says, though, there is no method for finding all roots of an arbitrary function. One reason that this is impossible is because some functions have infinite roots, arbitrarily close together, even on a finite interval. Examples are f(x)=0 or f(x)=sin(1/x)
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