Polynomial basis conversion made stable by truncated singular value decomposition (Q1384387)

The aim of this paper is to provide a numerically stable method for the transformation between the power and the Bernstein basis resp. the Bernstein and the B-spline basis. Although this transformation process is defined by a system of linear equations, the direct use of this linear system is sometimes not recommended, since it may be ill conditioned. The author of this paper proposes a method for the regularization of this transformation process, based on truncated singular value decomposition. The idea is described in some detail, and illustrated by two examples and a total of 17 figures.