How can I find the Proper starting point in FindRoot command?

[Mona_r]

Hi

I have some problems in finding the proper starting value in FindRoot[] command.
Cause I don't know exactly what the point is,I can't get the right answer!
How can I find roots without having the starting point?

Thanks

 

[who_]

Well, what is the FindRoot command? What are you referring too?

Anyways, I assume you are talking about a popular, well known analytical algorithm like Newton's method. For these methods, you NEED a starting point. The crucial idea behind these algorithms is that you start somewhere, and using information relating to the gradient of the function, you hone in on a root (if possible - consider f(x) = x^(1/3)). It is like finding a maximum or minimum of a function. These algorithms take a local search approach, so there is no way to take on a global perspective.

Thus, if your function has several roots, you can only find one of them at a time, and you can only find a specific root given that you starting point is sufficiently close to it.

 

[Mona_r]

It's something like this:
Table[FindRoot[(a function of variable x containing Bessel functions==0),{x,k[]}],{i,1,N}]
I gave one starting point but I couldn't get the proper solution!
I just want to know if there is another command for calculating these kind of equations or not?

thanks a lot

 

[who_]

Well, what software are you using? It would help if you specify the environment in which you are working.

 

[Mona_r]

Mathematica 6

 

[who_]

Well, you could check the Mathematica manual. You could automatically have it give itself a random starting point with some code, but I highly doubt that is what you want and I highly doubt that will be useful. I also would think that if Mathematica had such a function (I don't doubt one exists), it would simply give arbitrary starting positions anyways.

Like I said, the FindRoot function utilizes an analytic approach that REQUIRES a starting point. Look up Newton's method and the like to see how they work - they all depend on a good starting point.

 

[HallsofIvy]

Make an educated guess! You should be able to at least approximate a root for an equation. Try it. While I don't know precisely which algorithm is used, it is probably an iterative method and if it does not converge to a solution it does not converge. So 'make a guess' and if it does not give an answer- make another guess!

 

[Mona_r]

Thanks dears
I'm going to try these suggestions.
Good luck :-)