Construction of B-splines for generalized spline spaces generated from local ECT-systems
The authors study the construction of local support bases for generalized spline spaces. Such spaces are constructed by pasting together smoothly linear combinations of local ECT-systems, in the sense of Karlin and Studden. They discuss interpolation properties of generalized splines with respect to Hermite-type interpolation and suitable nodes. They extend the method due to Jetter et al to count the zeros of polynomial splines to generalized splines, and they use it to find generalized spline spaces allowing Hermite-type interpolation at suitable nodes. Such spaces are called interpolation spaces or IP-spaces for short. They are going to show that for them construction of local support bases is possible. For them, a basis of splines having minimal compact support is constructed. These functions are called B-splines and are obtained by solving certain interpolation problems.
scientific article; zbMATH DE number 2006397
scientific article