On 9/4/2003 2:12:47 PM, lbond wrote:
>On 8/23/2003 10:41:13 AM, jmG wrote:
>>I have added the second
>>method. It goes well with
>>Robert technique to SQUARE
>>ROOT for the index of
>>refraction. In the case of
>>T/C, the Y/X technique
>>is of extraordinary
>>efficiency.
>>We use commonly in finding
>>best approximations.
>>Usually, one more term in an
>>approximation
>>increases accuracy by 10
>>(typical of polynomials)
>>Here, we don't add one term,
>>but only one operation.
>>We increase accuracy by ~ 200
>>! ... remarkable.
___________________________
> Leslie replied:
>Remarkable indeed. A few things about
>this - first, why does this work?
>
>Second, although it's not your problem,
>I used the transformed data with
>rationalfit and I couldn't get the same
>accuracy out, which is very disturbing
>indeed. Supposedly the rationalfit
>function does exactly what Robert's
>"magic genfit" thing does, but with a
>"better" solver, only it's not. I've
>reported it to the developers, but it's
>deeply disturbing to me...
>____________________________
Leslie,
I think you will be Grand Mother before we finish the DataAnalysis pack !
You are right, there is miscarriage in the rationalfit. It does not implement completely Robert's "magic genfit". If it would be so, we would then get ~ same fit in the transformed data set with same NUM/DENOM order. Like you say: disturbing.
Check that one too: in theory we could increase the order up to rows(data)-1... at order 10, it start telling "undetermined fit" ???
For your first question: why does it work ?
Rational interpolation is the ideal method for curves that exhibit 1/x function. Which is also the best format for Thiele. Those format, polynomials don't approximate. Then the transformation Y/X for that particular case produces a very good new set, for rational fit.
The problem is the algorithm that is unclear versus Robert method. This is demonstrated in the attached work sheet.
Hope it will work sometimes.
jmG