🚀 go-pugleaf

In article <LSTERN.92Oct15162328@orville.nas.nasa.gov> lstern@orville.nas.nasa.gov (Louis G. Stern) writes:
>	Stuff Deleted
>
> Has anyone
>come across some combination of splines + least-squared fitting before?
>
	In developing a plotter algorithm for my PLOT program, I implemented
a piecewise least squares fit of cubic polynomials to the "local" data. The
usual least squares algorithm was subject to 2 constraints i.e. the cubic
had to be continuous in value and gradient with the previous cubic - as
indeed are cubic splines. These constraints are coded by means of Lagrange
multipliers - so that to obtain the next cubic, I had to invert a 6x6 matrix
(instead of the usual 4x4). The first 4 elements of the 6-vector are the
cubic coeffs one desires and the last two are the Lagrange multipliers that
are of no further use. To start it off, I do a normal unconstrained cubic fit
to the leftmost local data - so that this technique is not as nicely symmetric
as a normal cubic spline. I also used a "Lorentzian" weighting function to
weight the "local" points the width of which I could choose. For narrow widths
the piecewise polynomial fit curve makes valiant efforts to pass very close
to every point (like cubic splines) but for larger widths it produces a
smoother curve that ignores high frequency (noise?) in the data.

	Although this technique is fairly "obvious" I have never seen any
textbook refer to it - but I dare say someone out there may know better.

				Regards,	W. Alan B. Evans
						[ wabe@ukc.ac.uk ]