De Boor's algorithm: Difference between revisions

Revision as of 15:09, 10 October 2016

Revision as of 00:12, 17 January 2017

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== The algorithm ==

We can compute the above <math>\mathbf{s}(x)</math> by defining some <math> x \in [u_{\ell},u_{\ell+1}) </math>, setting <math> \mathbf{d}_i^{[0]} = \mathbf{Nd}^0_i(x)_i</math> for <math>i = \ell-n, \dots, \ell</math>, and with these, computing:

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