FindRoot repeatedly evaluating function

• To: mathgroup at smc.vnet.net
• Subject: [mg121052] FindRoot repeatedly evaluating function
• From: Simon Pearce <Simon.Pearce at nottingham.ac.uk>
• Date: Thu, 25 Aug 2011 07:05:19 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```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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