On rational B-splines with prescribed poles

Spaces of rational splines of maximal smoothness are considered which are constructed from certain rational functions with prescribed poles. For them a basis of splines having minimal compact supports was constructed in the literature. These functions which are called rational B-splines are obtained by solving certain linear equations with a block matrix depending on a parameter epsilon > 0. It is shown that in the limit epsilon --> 0 they tend to certain polynomial B-splines. (C) 2003 Elsevier B.V. All rights reserved.