       Re: Extrema of 2D Interpolating function

• To: mathgroup at smc.vnet.net
• Subject: [mg91440] Re: [mg91435] Extrema of 2D Interpolating function
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 22 Aug 2008 03:10:25 -0400 (EDT)

```Use FindRoot

approx[x_, base_] := RootApproximant[x/base, 2]*base

data = Flatten[Table[{{x, y}, Sin[x] Sin[y]},
{x, 0, 2 Pi, Pi/3}, {y, 0, 2 Pi, Pi/3}], 1];

f[x_, y_] = Interpolation[data][x, y];

Plot3D[f[x, y], {x, 0, 2 Pi}, {y, 0, 2 Pi}]

soln = FindRoot[{D[f[x, y], x] == 0, D[f[x, y], y] == 0},
{{x, #[]}, {y, #[]}}] & /@
{{1, 1}, {1, 5}, {3, 3}, {5,
1}, {5, 5}};

soln /. n_?NumberQ :> approx[n, Pi]

{{x -> Pi/2, y -> Pi/2}, {x -> Pi/2, y -> (3*Pi)/2}, {x -> Pi,
y -> Pi},
{x -> (3*Pi)/2, y -> Pi/2}, {x -> (3*Pi)/2, y -> (3*Pi)/2}}

Bob Hanlon

---- Modeler <eabad at ulb.ac.be> wrote:

=============
Hi, I'd like to compute the minima  and the saddle points of a 2D interpolating function f[x,y] obtained from a list of points with mathematica 6.0 (if possible in a specified x-y range0. The Nsolve standard routines do not seem to work in this case. Can anyone help? Thanks in advance.

```

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