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I have two polynomial interpolations of raw data:

  1. Wind speed as a function of turbine rotation => v(r)
  2. Power as a function of turbine rotation => p(r)

I would like to map these functions to a function describing the relationship between wind speed and power, specifically, p(v)

To provide more information, we are trying to compare the performance of two types of machines. The parameter rotation (r) has little to do with the performance, we are more-so interested in the relationship between v and p.

These are the relationships concerned:

Power vs RPM enter image description here

RPM vs Wind speed enter image description here

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    To straighten things out: you have a *parametric equation* for the curve relating wind speed and power, with turbine rotation as parameter, and you want the explicit relationship between wind speed and power. Right? Now... why BTW did you use polynomials? Did the physics of the situation necessarily dictate that you use interpolating polynomials?2011-10-06
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    @J.M. I have edited the question to provide more info. There is no strict dependence on polynomials, I find however on small intervals the interpolations can made quite accurate.2011-10-06
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    Do you have the polynomials v(r) and p(r) strictly by interpolation of the empirical data or do you have some additional theoretical/mathematical background for them? If they are simple polynomial regressions from the pairs of measures of (*r* and *v*) and of (*r* and *p*), and if the regressions are moreover based on the same set of data in *r*, then why not simply regress (polynomially) *p* on *v* ? Or is there some aspect why this would not be meaningful?2011-10-06
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    Huh. I would hope that there's a firm theoretical foundation behind your use of polynomials. You have *noisy* data; I will presume that you merely erroneously referred to your polynomial **fits** as "interpolations"... but seriously, have you tried looking for theoretical models? (In short, I fear your problem is more physical than mathematical.)2011-10-06
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    @J.M. I do not use the entirety of the data set, outliers are ignored and the average is taken, the interpolation is calculated based on that in MATLAB2011-10-06
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    "outliers are ignored" - oh boy... that's an entirely different can of worms. By what criterion are you ignoring them? Do you have a good grasp of the probability distribution the noise in your data follows?2011-10-06
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    upps - my previous comment asks before I saw the other comments and the update of your question. After seeing the pictures I wonder whether a polynomial regression of *p* on *v* where *r* is partialled out would be the most sensical thing ...2011-10-06

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