Stabilization of spline bases by extension

Abstract We present a method to stabilize bases with local supports by means of extension. It generalizes the known approach for tensor product B-splines much broader class functions, which includes hierarchical and weighted variants polynomial, trigonometric, exponential splines, but also box T-splines, other function spaces interest basis. Extension removes elements that cause instabilities from given basis linking them remaining ones specific linear combination. The two guiding principles this process are locality persistence. Locality aims at coupling functions whose close together, while persistence guarantees set globally supported like certain monomials in case polynomial remain span after Furthermore, we study how extension influences approximation power condition Gramian matrices associated basis, series examples illustrating potential method.