\nu.$$ The coefficients $y_j$ can be computed by solving the linear system $$A y = g,$$ where $A$ is the so-called *collocation matrix* containing the values of the basis functions at the interpolation nodes $$a_{ij} = f_j(\tau_i).$$ If the basis functions are linearly independent on $\{ \tau_1, \ldots, \tau_{\nu} \}$, the matrix $A$ is nonsingular, and the interpolation problem has a unique solution for all functions $g$.

The sensitivity of the solution is then determined by the condition number $\kappa_p(A)$ of the collocation matrix $$\kappa_p(A) = \| A \|_p \| A^{-1} \|_p,
  \label{1.1}$$ where $\| \ \|_p$ denotes the standard operator $p$-norm, with $1 \leq p \leq \infty$.

The polynomial B-splines of a fixed degree $d$ are frequently used as the basis functions in practice. Such a basis is uniquely determined by a given multiset of knots that defines the local smoothness of the basis functions. The corresponding collocation matrix is always totally nonnegative (see [@deBoor-2001; @Schumaker-2007]), regardless of the choice of the interpolation nodes.

A particular choice of nodes is of special interest, both in theory and in practice, for shape preserving approximation. When the nodes are located at the so-called Greville sites, i.e., at the *knot averages*, the 