Minimizing the condition number of a Gram matrix. (English) Zbl 1220.65055
The authors consider the problem of finding a set of points and/or weights which minimizes the condition number of the Gram matrix, \(k(A(x))\), defined by a polynomial basis. They propose a smoothing function for \(k(A(x))\) and show various properties of the smoothing function which ensure that a class of smoothing algorithms for solving the \(k(A(x))\) minimization problem converges to a Clarke stationary point globally.
Reviewer: Constantin Popa (Constanţa)
MSC:
65F35 | Numerical computation of matrix norms, conditioning, scaling |
90C26 | Nonconvex programming, global optimization |
15A12 | Conditioning of matrices |
15B57 | Hermitian, skew-Hermitian, and related matrices |