Re: Rationalized Fitting

• To: mathgroup at smc.vnet.net
• Subject: [mg125446] Re: Rationalized Fitting
• From: Ray Koopman <koopman at sfu.ca>
• Date: Wed, 14 Mar 2012 00:39:00 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jhienb\$b3o\$1@smc.vnet.net> <jjmuv3\$cen\$1@smc.vnet.net>

```On Mar 13, 1:02 am, Antonio Alvaro Ranha Neves <ane... at gmail.com>
wrote:
> No reply? Guess it's harder than it looks.
>
> On Thursday, February 16, 2012 9:28:27 AM UTC+1,
> Antonio Alvaro Ranha Neves wrote:
>
>> 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

Two things. First, the data you generate has multiplicative error,
so you should specify Weights->(1/#&) in NonlinearModelFit.

Second, it's not clear what you want or how the standard errors of
the parameter estimates relate to it.

```

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