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Rationalized Fitting

• To: mathgroup at smc.vnet.net
• Subject: [mg124987] Rationalized Fitting
• From: Antonio Alvaro Ranha Neves <aneves at gmail.com>
• Date: Thu, 16 Feb 2012 03:27:25 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello group members and advanced users,

Recently, I was trying to obtain the best fitting function with rational parameters, without success. I tried something like,

NoisyParabola = 
 Table[{x, (Prime[7]/Prime[8] + x Prime[9]/Prime[10] + 
      Prime[11]/Prime[12] x^2)*RandomReal[{.95, 1.05}]}, {x, 1, 10, 
   1/4}]
NLMFit = NonlinearModelFit[NoisyParabola, 
  Rationalize[a, 10^-6] + x Rationalize[b, 10^-6] + 
   Rationalize[c, 10^-6] x^2, {a, b, c}, x] 
NLMFit["ParameterTable"]

The main idea is to obtain the fitting coefficients (a,b,c) whose standard deviation (da,db,dc), would yield a fitting result of a best fit rational Rationalize[a,da]. But I fail to see how I can get this interactively.

Hope I made myself clear,
Thanks,
Antonio