The Numerical Evaluation of <i>B</i>-Splines

Abstract

The conventional method of evaluating B-splines by means of divided differences is numerically unstable. A relation between B-splines of consecutive degrees is derived which enables B-splines to be evaluated in a stable and efficient fashion. Analyses of error growth in the conventional and the stable methods are carried out. For the stable method an a priori relative error bound is obtained.