On Some Generalizations of B-Splines
This is a theoretical contribution for mathematicians working in spline theory and fractal interpolation, but it is incremental as it extends known concepts without demonstrating new applications or performance gains.
The paper reviews generalizations of B-splines to complex orders and constructs uncountable families of fractal functions from polynomial and exponential B-splines, extending fractal interpolation to unbounded supports. No concrete numerical results are provided.
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable families of self-referential or fractal functions from polynomial and exponential B-splines of integral and complex orders. As the support of the latter B-splines is the set $[0,\infty)$, the known fractal interpolation techniques are extended in order to include this setting.