The convergences of three L1 spline methods for scattered data interpolation and fitting using bivariate spline spaces are studied in this paper. That is, L1 interpolatory splines, splines of least absolute deviation, andL1 smoothing splines are shown to converge to the given data function under some conditions and hence, the surfaces from these three methods will resemble the given data values...

Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate Rn. This paper presents simple, geometric criteria that imply that, for regular shift-invariant tessellations, only a small subset of such spline families yield nested spaces: primarily the well-known tensor-product and box splines. Among the many nonrefinable constructions are hex-splines and thei...

In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S d , of cardinal polynomial splines of class C and degree d. Next, we show that the approximation order in the space generated by the integer translates of th...

*Department of Health Services Administration, Graduate School of Public Health, University of Puerto Rico Medical Sciences Campus, San Juan, Puerto Rico; †Cancer Control and Population Sciences Program, University of Puerto Rico Comprehensive Cancer Center, San Juan, Puerto Rico; ‡Department of Biostatistics and Epidemiology, Graduate School of Public Health, University of Puerto Rico Medical ...

the growing scarcity of fresh water is driving the implementation of wastewater treatment and water reuse on an increasingly large scale. various methods have been developed and used for water reuse from wastewater; however, the membrane distillation (md) process, as a promising separation technology, has recently gained more attention. the md process is a non-isothermal membrane-based separati...

Bivariate quadratic simplicial B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a Cl-smooth surface. The generation of triangle vertices is adjusted to the area1 distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-s...