**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 $\Omega\subset\RR^n$,
$n\ge2$.

**Preprint version available:** pdf

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