De Boor's algorithm: Difference between revisions

Revision as of 20:27, 3 May 2009

Revision as of 22:02, 4 June 2009

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Suppose <math> x \in [u_{\ell},u_{\ell+1}] </math> and <math> \mathbf{d}_i^{[0]} = \mathbf{d}_i </math> for <math>i = \ell-n, \dots, \ell</math>.

Now calculate

:<math> \mathbf{d}_i^{[k]} = (1- \alpha_{k,i}) \mathbf{d}_{i-1}^{[k-1]} + (1-\alpha_{k,i}) \mathbf{d}_i^{[k-1]}; \qquad k=1,\dots,n; \quad i=\ell-n+k,\dots,\ell </math>

with

:<math> \alpha_{k,i} = \frac{x-u_i}{u_{i+n+1-k}-u_i}. </math>