  Multi-degree splines are piecewise polynomial functions having sections of
different degrees. They offer significant advantages over the classical
uniform-degree framework, as they allow for modeling complex geometries with
fewer degrees of freedom and, at the same time, for a more efficient
engineering analysis. Moreover they possess a set of basis functions with
similar properties to standard B-splines. In this paper we develop an algorithm
for efficient evaluation of multi-degree B-splines, which, unlike previous
approaches, is numerically stable. The proposed method consists in explicitly
constructing a mapping between a known basis and the multi degree B-spline
basis of the space of interest, exploiting the fact that the two bases are
related by a sequence of knot insertion and/or degree elevation steps and
performing only numerically stable operations. In addition to theoretically
justifying the stability of the algorithm, we will illustrate its performance
through numerical experiments that will serve us to demonstrate its excellent
behavior in comparison with existing methods, which, in some cases, suffer from
apparent numerical problems.
