5 An overview of auto-folder development

The ideal solution to the problem of minimizing functions defined over noisy data is to use methods based on integral techniques, and we have chosen a method based on the Fourier decomposition of rotation curves. Because of the necessarily detailed nature of the following auto-folder development, it is useful to begin with a section-by-section overview of the process:

• Sect. 6: Define a basic folding method based upon a Fourier decomposition of a rotation curve. This gives the Mk I auto-folder;
• Sect. 7: Refine the basic method by optimizing the number of Fourier modes to be used for the decomposition of any given rotation curve. This gives the Mk II auto-folder;
• Sect. 8: Remember that, by the considerations of Roscoe 1999A (see also Appendix B), the interiors of rotation curves generally behave differently from their exteriors. So, consider the possibility that this differential behaviour might be due to noisy disturbance induced by the proximity of the central bulge, and therefore accountable in the folding process by removing the noisy interior sections - a process termed as "hole-cutting'';
• Sect. 9: Modify the Mk II auto-folder by a global implimentation of the hole-cutting process to obtain the Mk III auto-folder;
• Sect. 10: Compare the folding solutions with and without hole-cutting, and note that the effectiveness of the hole-cutting process appears to be $\ln A$ dependent;
• Sect. 11: Investigate the $\ln A$ dependency of hole-cutting effectiveness;
• Sect. 12: Refine the application of the hole-cutting process according the results of the latter invetsigation to obtain the Mk IV auto-folder.