Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms ba...

gravity acceleration data have grand pursuit for marine applications. due to environmental effects, marine gravity observations always hold a high noise level. in this paper, we propose an approach to produce marine gravity data using satellite altimetry, high-resolution geopotential models and harmonic splines. on the one hand, harmonic spline functions have great capability for local gravity ...

 This paper deals with a short term forecasting non-stationary time series using wavelets and splines. Wavelets can decompose the series as the sum of two low and high frequency components. Aminghafari and Poggi (2007) proposed to predict high frequency component by wavelets and extrapolate low frequency component by local polynomial fitting. We propose to forecast non-stationary process u...

This article provides a survey on modern methods of regional gravity field modeling on the sphere. Starting with the classical theory of spherical harmonics,weoutline the transition towards space-localizing methods such as spherical splines and wavelets. Special emphasis is given to the relations among these methods, which all involve radial base functions. Moreover, we provide extensive applic...

in this paper, we solve a linear system of second-order boundary value problems by using the quadratic b-spline nite el- ement method (fem). the performance of the method is tested on one model problem. comparisons are made with both the analyti- cal solution and some recent results.the obtained numerical results show that the method is ecient.

In the rst part of the paper, the problem of deening multi-variate splines in a natural way is formulated and discussed. Then, several existing constructions of multivariate splines are surveyed, namely those based on simplex splines. Various diiculties and practical limitations associated with such constructions are pointed out. The second part of the paper is concerned with the description of...

s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from R. ECT-spline curves in R are constructed by glueing together at interval endpoints generalized polynomials generated from different local ECT-systems via connection matrices. If they are nonsingular, lower triangular and totally positive there is a basis...

Cory D. Hauck Computational Mathematics Group Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge, TN 37831 USA ‡ We present a novel application of filters to the spherical harmonics (PN) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) pr...