#378 Some polynomial fit equations produce incorrect an plot.

[David Benn]

Compare the 7 degree polynomial fit of omi Cet data (see attached). The fit is fine but the equation is clearly wrong. Also, the zero point being subtracted from each time parameter is near the mid-point of the date range.

Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which is correct. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data; a short filtered single-cycle section was filtered for analysis. What would this look like if the whole FITS file's range was used?

[David Benn]

[David Benn]

• Description has changed:

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 Compare the 7 degree polynomial fit of omi Cet data (see attached). The fit is fine but the equation is clearly wrong. Also, the zero point being subtracted from each time parameter is near the mid-point of the date range.

-Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which looks fine. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data.
+Compare this to the 23 degree polynomial fit of Kepler RR Lyr data, which is correct. The zero point being subtracted from each time parameter is near the start of the date range. The other major difference is that it is quite a short range compared to the omi Cet data; a short filtered single-cycle section was filtered for analysis. What would this look like if the whole FITS file's range was used?

• Priority: 8 --> 9

[David Benn]

[Doug Welch]

Comment: High-order polynomials produce very, very large (t-t0)**n terms. To produce precision, the best strategy is to always make t0 the mid-time of the series.

[David Benn]

Doug, would you recommend the mid-point element, i.e. t[size(t)/2] or the mean time value, i.e. sum(t)/size(t)?

[Doug Welch]

Hi David, I would recommend the mean time value. All coefficients will be determined with maximum possible precision in that case, since the largest abs(t-tmean) will be smaller that the largest abs(t - t[size(t)/2]).

[David Benn]

Thanks Doug. That's what I was wondering too and it makes sense. I suppose that for some particular distributions of times, these values could be equivalent, but not in the general case.

[Doug Welch]

Hi David - I expect that you are well aware of how to nest polynomial calculations to maintain precision since you are a skilled programmer.
But if that doesn't sound familiar, let me know!

[David Benn]

Hi Doug. If you're referring to Horner's method/scheme/rule, then yep. I can generate this form of the polynomial equation in the model dialog.

[David Benn]

For various reasons, including the stability, and ability to determine derivatives and apply optimisation algorithms, the current TS based polyfit implementation will probably be replaced by the apache commons math implementation. This will also allow me to add extrema finding and goodness of fit functionality for EB and other analysis.

[David Benn]

Implemented in https://sourceforge.net/p/vstar/code/1009

[David Benn]

Horner's form will be added as a checkbox-selectable alternative in future. A key issue was ensuring sufficient precision in coefficients.