On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis
Copyright policy )On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis
The authors recall the definition of the \(p\)-norm condition number and state some facts about the multivariate Bernstein basis. In particular, they study the 2-norm case. The condition number can then be computed exactly from the eigenvalues of the Gram matrix of the Bernstein basis. They show that the condition number for fixed \(s\) grows like \(O(n^s 2^n)\), as \(n\) increases. They end the paper with an appendix on the connection between Bernstein and Legendre polynomials on simplices.
- University of Oslo Norway
- University of Bonn Germany
Polynomial approximation, Applied Mathematics, Numerical computation of matrix norms, conditioning, scaling, Multidimensional approximation, Computational Mathematics, Approximation by polynomials, multivariate Bernstein basis, Error analysis, Algorithms for approximation of functions, multidimensional approximation, Condition number, approximation, error analysis, condition number
Polynomial approximation, Applied Mathematics, Numerical computation of matrix norms, conditioning, scaling, Multidimensional approximation, Computational Mathematics, Approximation by polynomials, multivariate Bernstein basis, Error analysis, Algorithms for approximation of functions, multidimensional approximation, Condition number, approximation, error analysis, condition number
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