An Optimal Property of B-Bases for the Modified Richardson Method

Abstract

A space with a normalized totally positive basis has a unique normalized B-basis. In computer-aided geometric design, normalized B-bases present optimal shape-preserving properties. More optimal properties of normalized B-bases were proved previously. This paper provides a new optimal property concerning the modified Richardson iterative method when applied to collocation matrices of normalized B-bases. Moreover, a similar optimal property is proved for the tensor product of normalized B-bases.

Keywords

• modified Richardson method
• B-bases
• totally positive matrices