9 The Mk III auto-folder

Figure 5:
Comparison of Mk II and Mk III auto-folder solutions.
The vertical lines indicate the positions of the A, B, C, D and E peaks in
the PS solution |

9.1 Algorithmic definition of the Mk III auto-folder

- For any given rotation curve, fold using the Mk II auto-folder;
- record the number of Fourier modes used for this fold, say , and the estimates for and ;
- apply the hole-cutting algorithm defined Roscoe 1999A to this folded rotation curve, and record the removed points;
- take the original
*unfolded*rotation curve, and reduce it by removing these recorded points; - fold this reduced rotation curve using the Fourier method already described, but taking care to redefine the Fourier coefficients in the manner described in the next subsection;
- for this second-stage folding process, use either the modes recorded at the first-stage folding process, or the number of modes defined by the algorithm of Sect. 6.2, whichever is the least;
- use the recorded estimates for and as the initial guess for the minimization process of this second-stage folding.

where

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