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

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In summary, the conversation discusses the difficulty of finding the proper starting value in the FindRoot[] command and the necessity of a starting point for analytical algorithms like Newton's method. The conversation also mentions using a random starting point or making an educated guess to approximate a root.
  • #1
Mona_r
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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! :cry:
How can I find roots without having the starting point?

Thanks
 
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  • #2
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.
 
  • #3
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
 
  • #4
Well, what software are you using? It would help if you specify the environment in which you are working.
 
  • #5
Mathematica 6
 
  • #6
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.
 
  • #7
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!
 
  • #8
Thanks dears
I'm going to try these suggestions.
Good luck :-)
 

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

What is the purpose of the FindRoot command in scientific research?

The FindRoot command is a function in mathematical software, such as Mathematica, that is used to find the root of a given equation or system of equations. It is commonly used in scientific research to solve for unknown variables or to find the optimal solution for a given problem.

2. How do I determine the proper starting point for the FindRoot command?

The proper starting point for the FindRoot command can be determined by analyzing the given equation or system of equations. It is recommended to choose a starting point that is close to the actual root or solution, as this will increase the chances of finding the correct solution in a shorter amount of time.

3. What happens if I choose an incorrect starting point for the FindRoot command?

If an incorrect starting point is chosen for the FindRoot command, it may result in an incorrect solution or the command may fail to find a solution altogether. It is important to carefully analyze the equation and choose a starting point that is as close to the actual root as possible.

4. Can I use multiple starting points in the FindRoot command?

Yes, it is possible to use multiple starting points in the FindRoot command. This can be useful in cases where the equation has multiple roots or when the starting point is not known. The command will then try each starting point until it finds a solution or until the maximum number of iterations is reached.

5. Are there any tips for choosing the proper starting point in the FindRoot command?

One tip for choosing the proper starting point in the FindRoot command is to plot the equation or system of equations and visually identify where the root may be located. Another tip is to use a combination of analytical and numerical methods to estimate the root and use that as the starting point. It may also be helpful to try different starting points and compare the results to ensure the accuracy of the solution.

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