On the \(p\)-norm condition number of the multivariate triangular Bernstein basis (Q1576462)

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.