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Optimally stable multivariate bases. (English) Zbl 1041.65017
For spaces of multivariate polynomials and multivariate splines, bases of triangular Bernstein polynomials and tensor product B-splines are most useful due to a variety of their properties. Among those, the nonnegativity or even a partition of unity property are important. In this paper, their numerical stability/conditioning is shown to be optimal as a new important aspect.

MSC:
65D07 Numerical computation using splines
41A10 Approximation by polynomials
41A15 Spline approximation
41A63 Multidimensional problems
65F35 Numerical computation of matrix norms, conditioning, scaling
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