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### Re: Re: Estimating continuous functions

by Itatsumaki (Friar)
 on Mar 29, 2004 at 17:43 UTC ( #340688=note: print w/replies, xml ) Need Help??

in reply to Re: Estimating continuous functions

Isn't Runge-Kutta a method for numeric integration of known curves? I think essentially you're suggesting to regress a high-order Runge-Kutta and then minimize the differential area. That's an interesting approach, but I suspect pretty computationally slow compared to directly fitting splines or something like that. I suspect the OP would be better off doing direct interpolation instead, especially because Runge-Kutta won't allow for extrapolation beyond predicted values.

One other note: remember that if you try to estimate a high-order equation without a lot of input data, you can run into over-fitting problems. Most numerical techniques get much more accurate (and slower) with lots of data

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Re: Re: Re: Estimating continuous functions
by thor (Priest) on Mar 30, 2004 at 12:35 UTC
Runge-Kutta is a method for solving differential equations numerically. However, there is a mapping from integrals to differential equations, so in that respect Runge-Kutta is also a method for solving integrals numerically.

thor

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