Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (1978,1983) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local properties. The source of this problem is the use of a ...

Recently, we have introduced spaces of splines deened on triangulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangula-tions. ...

In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical...

We compare univariateL1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than...

David Owen (Owen D)1, Joseph Ferguson (Ferguson J)2, Benjamin Keaton (Keaton B)2, Rodney Hansen (Hansen R)2, Gregory Norris (Norris GH)3 and David Aguilar (Aguilar D)2 1Department of Bachelor of Integrated Studies, Weber State University, Ogden, UT 84408 2Department of Athletic Training and Nutrition, Weber State University, Ogden, UT 84408 3Department of Nutritional Sciences, University of Con...

Ferguson and Henderson (1947) described the isolation of a motile coliform organism possessing the major somatic antigen of Shigella sonnei, form I, from the feces of a patient whose clinical history was not available. They called the organism strain C27. It was also found in man and animals by Wheeler (1947), van de Pitt (1953), and Schmid, Velaudapilli and Niles (1954). Recently, similar orga...

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary twodimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize current l...

The definition of a B-spline is extended to unordered knot sequences. The added flexibility implies that the resulting piecewise polynomials, named U-splines, can be negative and locally linearly dependent. It is therefore remarkable that linear combinations of U-splines retain many properties of splines in B-spline form including smoothness, polynomial reproduction, and evaluation by recurrence.