This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. ...

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...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...

When fitting a parametric curve through a sequence of points, it is important in applications that the curve should not exhibit unwanted oscillations. In this paper we take the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points. From this point of view, we study periodic cubic spline interpolation and derive bounds on the dev...

A cubic spline regression model was used to fit the experimental open-circuit potential ~OCP! curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predict...

Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubi...

Orthogonal, semiorthogonal and biorthogonal wavelet bases are special cases of oblique multiwavelet bases. One of the advantage of oblique multiwavelets is the flexibility they provide for constructing bases with certain desired shapes and/or properties. The decomposition of a signal in terms of oblique wavelet bases is still a perfect reconstruction filter bank. In this paper, we present sever...

HB-splines: a Blend of Hermite splines and B-splines Laurent Grisoni Carole Blanc Christophe Schlick LaBRI [grisonijblancjschlick]@labri.u-bordeaux.fr Abstract This paper proposes to study a spline model, called HB-splines, that is in fact a B-spline representation of Hermite splines, combined with some restriction on the di erential values at segment boundaries. Although this model does not ap...