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Stable local bases for multivariate spline spaces

Davydov, Oleg (2001) Stable local bases for multivariate spline spaces. Journal of Approximation Theory, 111 (2). pp. 267-297.

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Abstract

We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.