       Re: FindRoot termination criteria

• To: mathgroup at smc.vnet.net
• Subject: [mg5561] Re: FindRoot termination criteria
• From: Robert Knapp <rknapp at sover.net>
• Date: Thu, 19 Dec 1996 01:02:47 -0500
• Organization: Wolfram Research
• Sender: owner-wri-mathgroup at wolfram.com

```Sysabel wrote:
>
> Could someone tell me what criteria is used in FindRoot to terminate
> the search?
> I'm running FindMinimum on
> a function that does not have local minima yet it terminates.  I've
> tried upping the MaxIterations and the AccuracyGoal but the results
> don't seem to improve.
>
> For example :
> numerical_solution = FindRoot[f[x]==0, {x, {0,1}},
> AccuracyGoal->0.001];
>
> If exact solution is name exact_solution,
>
> is Findroot exit the search when :
>         abs(numerical_solution - exact_solution) < 0.001 ???
> or when :
>         abs[f[numerical_solution ] - f[exact_solution]] < 0.001 ???
>
> or others ?
>
> Eric

It is hard to tell from your message whether you are wanting to use

FindRoot -- for numreically finding a solution to an equation..or
FindMinimum -- for numerically minimizing a function.

The criteria for both are based on the objective function.

For FindRoot, at the exact solution, the objective function is 0, so
the stopping criterion is that

Abs[f[numerical_solution]] <= 10^(-AccuracyGoal)

For FindMinimum, estimates are used so that

Abs[f[numerical_solution]-f[exact_solution]] <= 10^(-AccuracyGoal)

and (if f[exact_solution] is non zero)

Abs[(f[numerical_solution]-f[exact_solution])/f[exact_solution]] <=
10^(-PrecisionGoal)

FindRoot does not have a PrecisionGoal option because relative error at
zero makes no sense.

Rob Knapp
WRI

```

• Prev by Date: Re: RSolve question
• Next by Date: functionals
• Previous by thread: FindRoot termination criteria
• Next by thread: LaTeX COMPATIBLE MATHEMATICA FRONT END ?