Re: FindRoot repeatedly evaluating function

• To: mathgroup at smc.vnet.net
• Subject: [mg121070] Re: FindRoot repeatedly evaluating function
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 26 Aug 2011 05:23:10 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108251105.HAA24905@smc.vnet.net>

```FindRoot makes several evaluations near each guess to estimate the
derivative numerically, and uses that to compute another guess. There's
nothing odd or surprising about it.

To avoid all that (where possible), use symbolic solvers instead:

Solve[x[10] == 0 /.
First@DSolve[{x''[S] - x'[S] + x[S] == 0, x[0] == 1, x'[0] == a}, x,
S], a]

{{a -> (Csc[5 Sqrt[3]] (-3 Cos[5 Sqrt[3]] + Sqrt[3] Sin[5 Sqrt[3]]))/(
2 Sqrt[3])}}

Bobby

On Thu, 25 Aug 2011 06:05:19 -0500, Simon Pearce
<Simon.Pearce at nottingham.ac.uk> wrote:

> Hi Mathgroup,
>
> When I use FindRoot[f[y],y] I find that the inner function f is
> evaluated 3 or 4 times at each value of y (or at least very similar
> values), even if y is far from the root. This has obvious implications
> to the speed of my code.
> Can anyone explain why this is the case, and tell me any way to stop it
> from repeatedly evaluating f? If I use f[a]:=f[a]=... then it uses the
> stored result, but I don't want to store thousands of such real valued
> expressions.
>
> The following simple code shows the essence of the problem, using Print
> to show where the function is evaluated and its value there.
>
> f[a_?NumericQ]:=Module[{sol},
>   sol=NDSolve[{x''[S]-x'[S]+x[S]==0,x[0]==1,x'[0]==a},x,{S,0,10}][[1]];
>   Print[{a,x[10]/.sol}]; x[10]/.sol ]
> FindRoot[f[y],{y,6}]
>
> Thanks,
> Simon Pearce
> Postdoctoral Researcher
> The Centre for Plant Integrative Biology
> School of Biosciences
> University of Nottingham
>
>
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--
DrMajorBob at yahoo.com

```

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