       Re: optimization nested in root-finding

• To: mathgroup at smc.vnet.net
• Subject: [mg65137] Re: optimization nested in root-finding
• Date: Wed, 15 Mar 2006 06:29:51 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```On 3/14/06 at 5:59 AM, BoLe79 at gmail.com (Borut Levart) wrote:

>I was wondering what is the use of giving x two initial values, as
>{x, 3, 5} in the FindRoot example of Bob Hanlon above. I guess
>FindRoot can then work out with some other, more efficient
>algorithm. But I put StepMonitor :> Print[x] in the FindRoot, and
>the step count wasn't any smaller. And for some examples it
>wouldn't even be possible for FindRoot to find the solution with
>only a single starting value, I think.

The method FindRoot uses to isolate the root is different when using two initial values (which ideally should bracket the root). If you use the Help Browser to look up FindRoot and click on the link, Advanced Documentation, you will find a more complete discussion.

Note the number of steps used for a given method to locate the root will depend on the more than just the efficiency of the algorithm. With a good starting point, Newton's method is one of the more efficient algorithms in terms of the number of iterations required for a given accuracy. But another method such as the secant method my actually take less time to converge even though there may be more iterations, particularly if the derivative is time consuming to evaluate.
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