De Boor's algorithm: Difference between revisions

Revision as of 12:12, 30 January 2007

Revision as of 12:13, 30 January 2007

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== The algorithm ==

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

Now calculate

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