Approximation by linear combinations of multivariate B-splines

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...

Linear combinations of B-splines as generating functions for signal approximation

The advantages of B-splines for signal representation are well known. This paper explores a fact that seems to be less well known, namely, the possibility of using linear combinations of B-splines to obtain representations that are more stable than the usual ones. We give the best possible Riesz bounds for these linear combinations and calculate their duals, in a generalized sampling context. ...

Quasiinterpolants and Approximation Power of Multivariate Splines

The determination of the approximation power of spaces of multivariate splines with the aid of quasiinterpolants is reviewed. In the process, a streamlined description of the existing quasiinterpolant theory is given. 1. Approximation power of splines I begin with a brief review of the approximation power of univariate splines since the techniques for its investigation are also those with which...

Multivariate Splines for Data Fitting and Approximation

Methods for scattered data fitting using multivariate splines will be surveyed in this paper. Existence, uniqueness, and computational algorithms for these methods, as well as their approximation properties will be discussed. Some applications of multivariate splines for data fitting will be briefly explained. Some new research initiatives of scattered data fitting will be outlined. §

Bayesian regression with multivariate linear splines