Accurate computations with collocation matrices of a general class of bases

In this paper, we provide algorithms for computing the bidiagonal decomposition of the collocation matrices of a very general class of bases of interest in computer‐aided geometric design and approximation theory. It is also shown that these algorithms can be used to perform accurately some algebraic computations with these matrices, such as the calculation of their inverses, their eigenvalues, or their singular values. Numerical experiments illustrate the results.