Timeline for Polynomial approximations of curves

7 events

when toggle format	what		by	license	comment
Jun 7, 2016 at 0:39	comment	added	bubba		The projection property can't be used in general. Another common example is the intersection of a sphere and a cylinder (where the sphere center doesn't lie on the cylinder's centerline).
Jun 7, 2016 at 0:31	comment	added	bubba		Do you know if the Remez algorithm has been extended beyond the real-valued case?
Jun 7, 2016 at 0:30	comment	added	bubba		Generally, quadratic polynomials are not very useful for this sort of application. They are always planar, and the original curve obviously is not. But, your example is interesting, anyway. Actually, a quadartic curve is just a parabola, and a parabola can be made to interpolate four points. In general, interpolation might be a good approach -- it often produces approximants that are close to optimal, and with far less effort than the Remez algorithm. But, how to choose the points you interpolate??
Jun 7, 2016 at 0:25	comment	added	bubba		Thanks for your answer. There is indeed a well-known iterative scheme that works well in the real-valued case. It's called the Remez exchange algorithm. There's a lengthy discussion of it in M.J.D. Powell's book.
Jun 6, 2016 at 19:20	history	edited	Aaron Meyerowitz	CC BY-SA 3.0	added 915 characters in body
Jun 6, 2016 at 4:04	history	edited	Aaron Meyerowitz	CC BY-SA 3.0	added 1 character in body
Jun 6, 2016 at 3:54	history	answered	Aaron Meyerowitz	CC BY-SA 3.0