Talk:Interpolation
From Wikipedia, the free encyclopedia
Crikey! This page is strangely marked-up.
The section on cosine interpolation includes the following text
- This is a slight improvement over linear interpolation, the resulting function is continuously differentiable, but the differentiable is predictable since the interpolation still has only linear accuracy.
What does it mean that the differentiable is predictable? A reference for this method of interpolation would also be appreciated. -- Jitse Niesen 22:39, 23 May 2004 (UTC)
I removed the section on cosine interpolation. Searching for it on MathSciNet gives no hits, while I got hundreds for polynomial interpolation and spline interpolation. So it seems that cosine interpolation is not that important to be mentioned here. -- Jitse Niesen 22:13, 5 Jun 2004 (UTC)
There is such a thing as cosine interpolation, but in terms of its accuracy it is pretty much the same as linear interpolation but is more expensive to compute. Basically, it tries to avoid some of the artifacts created by linear interpolation by lending the function the continuous differentiability property of the cosine curve. My opinion is that the computational costliness involved is why you had difficulty finding it, cubic interpolation has a similar cost but is far more effective, so cosine interpolation has become a mathematical oddity with no real use. I believe what I have said has quite an overlap with the article. Apart from some diagrams and the equation to generate the function, I do not see what else could go into an article. However, I do think on principle even if this topic represents a mathematical evolutionary dead end there should be an article, for the clarification of a term that I assume from your research was difficult to find information on. Chadernook 23:30, 15 January 2007 (UTC)
Contents |
[edit] I cant find the topic "Spatial interpolation"
I was looking for information and techniques for Spatial interpolation and was surprised to see wikipedia, not having this topic.
Can anyone look into this?
Thanks.
[edit] Fix the table
Could someone who understands tables in html fix the table in the Example section? The columns are so close together that if 2 appears in the left column and −3 in the right, then it looks as if "2 − 3" appears there. Michael Hardy 00:37, 14 Feb 2005 (UTC)
- It should be better now. -- Jitse Niesen 17:21, 1 Mar 2005 (UTC)
[edit] Remark (moved from the article page)
But there are some cases where a polynom interpolate in end point. (anoninmous comment, moved from the article page by Oleg Alexandrov 19:44, 5 Jun 2005 (UTC))
[edit] Polynomial interpolation --> "infinitely differentiable"?
The section on polynomial interpolation states:
- "the interpolant is a polynomial and thus infinitely differentiable. So, we see that polynomial interpolation solves all the problems of linear interpolation."
This is referring to the remark that a linear interpolation cannot be differentiated at its endpoints. However, surely this is also the case for generalised polynomial interpolation?
Oli Filth 09:57, 15 October 2006 (UTC)
I may be wrong but at or beyond the endpoints of the interpolation I think it is still infinitely differentiable, but using the function here makes the process technically extrapolation? Chadernook 23:30, 15 January 2007 (UTC)
[edit] Legrange, anyone?
I find this page (and linked pages too, such as Linear interpolation, polynomial interpolation) to be too focussed on the practicalities of interpolation using computers, and too little on the mathematical theory of the subject. At the very least the foundations of the subject (Newton, Lagrange, Hermite, Bessel) should be covered, and references made to and analogies pointed out with the related subject of numerical integration.
