Accurate computations with Lupaş matrices

Lupaş q-analogues of the Bernstein functions play an important role in Approximation Theory and Computer Aided Geometric Design. Their collocation matrices are called Lupaş matrices. In this paper, we provide algorithms for computing the bidiagonal decomposition of these matrices and their inverses to high relative accuracy. It is also shown that these algorithms can be used to perform to high relative accuracy several algebraic calculations with these matrices, such as the calculation of their inverses, their eigenvalues or their singular values. Numerical experiments are included.