\(GB\)-splines of arbitrary order
The authors expand the main results of \textit{B. I. Kvasov} [Ann. Numer. Math. 3, No. 1-4, 139-149 (1996; Zbl 0873.65006)] to generalized \(B\)-splines (\(GB\)-splines) of arbitrary order. These \(GB\)-splines are nonnegative functions with supports of minimal length which form a partition of unity. Explicit formulae and recurrence relations for the calculation of \(GB\)-splines are given. The main properties of \(GB\)-splines and their series, such as partition of unity, shape-preserving properties, invariance with respect to affine transformations are derived. It is shown that the \(GB\)-spline series is a variation diminishing function and the systems of \(GB\)-splines are weak Chebyshevian systems.
generalized \(B\)-spline (\(GB\)-spline)
scientific article; zbMATH DE number 1367884