Talk:Linear interpolation

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(x-x0)/(x1-x0) is not the SLOPE! slope is rate of change in something. that is, it must have different units in numerator and denominator (ie, meters per second; rise/run; bps; etc). So it's misleading to call it slope. That, or i've gone crazy in the years since taking math classes.

You're not crazy, the page was wrong. Good catch. —Blotwell 10:50, 23 Jun 2005 (UTC)

[edit] Alphas

The alphas are only equal when the slope of the line you're trying to interpolate is one. Otherwise, they're not. --Herbchronic 00:48, 29 July 2006 (UTC)

Please explain. To me, the article seems correct on this account. -- Jitse Niesen (talk) 05:10, 29 July 2006 (UTC)

The article is correct: interpolation coefficient is different than slope

[edit] Appeal to Rolle's theorem

"It can be proven using Rolle's theorem that if f has two continuous derivatives, the error is bounded by..." I just tried this and it can't work. You have to use the mean value theorem, not Rolle's theorem - J Fellows, University of Birmingham

The proof I know uses Rolle's theorem. This proof is for polynomial interpolation in general, not just linear interpolation. It's in Atkinson's Introduction to Numerical Analysis, and also in Suli and Mayers' book with the same title. However, the proof uses some algebraic manipulations and the difference between Rolle's theorem and the mean value theorem is just one small step, so it's well possible that it's better to appeal to the mean value theorem. I wouldn't mind if you changed it. -- Jitse Niesen (talk) 03:22, 14 February 2007 (UTC)

Does "has two continuous derivatives" mean "has continuous first and second derivatives"? This does not say what it means, because "derivative" is ambiguous A well-behaved function f has one derivative (derivative function) and an infinite number of derivatives (of values of the derivative function at each point of its domain). — Paul G (talk) 10:20, 6 March 2008 (UTC)

Yes, "has two continuous derivatives" means "has continuous first and second derivatives". It's the only interpretation that makes sense, so I don't think it's really ambiguous. It's also a fairly common way to put it, but perhaps rather informal and I can see that it will confuse readers, so I changed it. -- Jitse Niesen (talk) 11:00, 6 March 2008 (UTC)