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How to include a constraint in NonlinearFit?

• To: mathgroup at smc.vnet.net
• Subject: [mg44647] How to include a constraint in NonlinearFit?
• From: "L. Vergara" <lvergara at lauca.usach.cl>
• Date: Wed, 19 Nov 2003 04:59:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

thanks to Curt Fisher, now I know how to to fit an array of preexisting
data with a function defined by NDSolve (see http://tinyurl.com/v0n1)

In the example I mentioned in my previous message, the function to be
fitted is

f[y_,a_,b_] :=NDSolve[x'[y] == (y^2/2 + a y + b)/Sqrt[1 -(y^2/2 + a y +
b)^2], x[0] == .6}, y, {y, 0, 1.5}];

Here there is a constraint that must be satisfied: Abs[(y^2/2 + a y
+b)^2]<1.
Do you know how include this into NonlinearFit (or perhaps better, into
NDSolve)?
Thanks!
Lautaro Vergara