A remark on B-splines

Expo-rational B-splines Expo-rational B-splines Expo-rational B-splines

A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Least squares cubic splines without B-splines

There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

Splines as Linear Combinations of B-splines. a Survey

The layout of the survey is as follows. After a short discussion of cardinal B-splines, i.e., of B-splines on a uniform knot sequence, in Section 2, B-splines for an arbitrary knot sequence are introduced in Section 3 and shown to be a basis for certain spaces of piecewise polynomial functions. Various simple properties of B-splines are listed in Section 4, and the relationship between a spline...

A remark on the definition of B-hyperpath

In this note we show that a commonly used definition of a hyperpath in a directed hypergraph is not correct. This is done by presenting a counter-example which fulfils the definition but is not a hyperpath.