Talk:Monotone cubic interpolation

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i want a f(x,y) that can cover a square of 1*1 sizs? 77.237.172.1 (talk) 20:35, 10 February 2008 (UTC)

Look at Multivariate interpolation. --Berland (talk) 07:20, 22 February 2008 (UTC)

[edit] Correctness of step 5

I reverted this edit, because it contradicts the referenced paper by Fritsch and Carlson, and because the claims put forward by the edit were unreferenced. The introduced comment may be correct, but if so it has to be referenced. --Berland (talk) 13:58, 20 February 2008 (UTC)

[edit] Re: Correctness of step 5

The Step 5, as it was originally put down, was misinterpreted. The original article by Fritsch & Carlson (1980) states the following Step 2A: find such subset L * of set L of all feasible parameters (α,β), which is defined by the conditions in Step 5, such that for any (\alpha,\beta)\in L^* and 0\leq\alpha^*\leq\alpha, 0\leq\beta^*\leq\beta, we have (\alpha^*,\beta^*)\in L^*. To preserve monotonicity of the previous interval, while updating values (α,β) in the current interval, we need to check that set L * , in our case defined by \alpha_k^2 + \beta_k^2 \leq 9, satisfies this condition. Note that we need to check conditions of this subset in Step 5, as well as normalizing the (α,β) when they fall outside of it. The original Wiki article showed inconsistent application of this argument.76.194.82.134 (talk) 01:57, 22 February 2008 (UTC)

Glad you cared to elaborate here. By rereading the paper, I see your point, and as far as I can see, in order for the wiki article to be correct in terms of the article, we should replace step 5 by:
5. Now, if \alpha_k^2 + \beta_k^2 > 9, then set mk = τkαkΔk and mk + 1 = τkβkΔk where \tau_k = 3(\alpha_k^2 + \beta_k^2)^{-1/2}.
--Berland (talk) 07:17, 22 February 2008 (UTC)
Thanks, Berland. Just corrected the article.159.53.110.143 (talk) 15:43, 22 February 2008 (UTC)

[edit] Higham 1992 suggests a possibly better alternative

Higham, D. J. (1992) Monotonic piecewise cubic interpolation, with applications to ODE plotting. Journal of Computational and Applied Mathematics, 39 (3). pp. 287-294. ISSN 0377-0427

They point out that if you *know* your derivatives and data at every point, there is a better way to ensure monotonicity than forcing the interpolant to have the wrong derivative at a data point: they introduce extra knots.

Might be worth mentioning.