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 ε>0. It is shown that in the limit ε→0 they tend to certain polynomial B-splines.