Talk:Polynomial and rational function modeling

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I've done a bit of work in this area and I am not sure if this would be the correct article or not to discuss methods of generating these models. One may build up function models from: local information (Taylor series and pade approximations), interval information (generalized fourier series and Chebyshev rational functions), and asymptotic behavior estimation.

I am not sure if anyone has any interest in such a discussion of modeling functions locally, over an interval, or asymptotically. I think it would be good for this section to discuss several approaches and their trade-offs.

I have found that building a Taylor-like series from orthogonal Chebyshev polynomials and converting to a pade-like approximation to be a very general powerful approach (see: Richard L. Burden and J. Douglas Faires, "Rational Function Approximation," in Numerical Analysis 9th edition, Brooks/Cole, ISBN-13:9780538733519, 2011. [Mouse7mouse9 03:19, 2 July 2014 (UTC)] — Preceding unsigned comment added by Mouse7mouse9 (talk • contribs)

A lot of lofty claims here on the utility of rational functions. From my experience I can say it's all half truths. For example, I recently worked on a problem where I applied the linear initialization, and that worked very poorly, but in other cases it works well. Extrapolation can work remarkably well if the fit is carefully tailored, on the hand if you're just using a nonlinear fit even interpolation can blow up (more likely as your dimensionality increases).

I'm not being specific, that's beside the point, the point I'm making is that this article makes it sounds like it can cure cancer without citations where in reality it's more like ibuprofen: can lessen pain, depending on situation.

There is a big bibliography here, but try actually finding anything about rational function fitting in it, you'll be unpleasantly disappointed.

Ben pcc (talk) 00:56, 18 June 2024 (UTC)[reply]