Stable numerical evaluation of multi-degree B-splines

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 freedom and, at same time, a more efficient engineering analysis. Moreover possess set basis similar properties to standard B-splines. In this paper we develop an algorithm evaluation multi-degree B-splines, which, unlike previous approaches, is numerically stable. The proposed method consists in explicitly constructing mapping between known and B-spline space interest, exploiting fact that two bases related by sequence knot insertion and/or degree elevation steps performing only stable operations. addition theoretically justifying stability algorithm, will illustrate its performance through numerical experiments serve us demonstrate excellent behavior comparison existing methods, some cases, suffer from apparent problems.