… basis on [0,1], see [2,9]. In this paper we extend some of the univariate results on optimal
stability to the multivariate … on , we say that a basis b ∈ B is optimally stable for the evaluation of …

… stable dual method for the solution. It is based on the knowledge of all dual feasible bases
under … Part 2 of the method enables us to compare the condition number of the “optimal” basis …

… is optimal (see [6]). In [7], a characterization of optimally stable bases of spaces of univariate
… On the other hand, the optimal stability of some bases of spaces of multivariate functions …

… that is stable in slightly acidic solutions because the protonation of several cytosine bases
to … C and pure spectra S T matrices, optimally fitting the experimental data matrix D using the …

… basis, it is well-known that the least-squares approximations can still become inaccurate when
the number of sample points M (from a suboptimal … We provide proof of the stability of the …

… )$|-orthonormal basis is not available, stable and quasi-optimally … basis of |$V_n$|
orthonormal in a discrete sense. The computational cost for the calculation of the surrogate basis …

… Bases optimally stable among all bases formed by nonnegative … of multivariate functions
[6]. In section 4 we prove that the basis used in the representation (1.1) has optimal stability …

… on optimal stability for spaces of univariate functions have been obtained in [12] and [13],
and examples of optimally stable multivariate bases … Bernstein basis is also optimally stable. …

… , in the sense that there does not exist (up to permutation and scaling) another basis of its …
corresponding multivariate Bernstein basis, although we can mention [7] about optimal stability …

… of a function expressed in terms of a given basis. Optimal bases with respect to the Farouki–…
We prove in Section 2 of this paper the optimal stability of the Lagrange representation with …