Optimal Stability of Bivariate Tensor Product Bases

We analyze some properties of bivariate tensor product bases. In particular, we obtain conditions so that a bivariate tensor product basis is optimally stable for evaluation. Finally, we apply our results to prove the optimal stability of tensor product bases of spaces containing algebraic, trigonometric and hyperbolic polynomials with a lot of interest in the representation of curves and surfaces in CAGD.

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