Approximation of noisy data using multivariate splines and finite element methods

Finite Element Approximation with Hierarchical B-Splines

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. §

Finite Element Methods with Hierarchical WEB-splines

Piecewise polynomial approximations are fundamental to geometric modeling, computer graphics, and finite element methods. The classical finite element method uses low order piecewise polynomials defined on polygonal domains. The domains are discretized into simple polygons called the mesh. These polygons might be triangles, quadrilaterals, etc., for two-dimensional domains, and tetrahedra, hexa...

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...

Splines and Finite Element Spaces

Splines are piecewise polynomial functions that have certain “regularity” properties. These can be defined on all finite intervals, and intervals of the form (−∞, a], [b,∞) or (−∞,∞). We have already encountered linear splines, which are simply continuous, piecewise-linear functions. More general splines are defined similarly to the linear ones. They are labeled by three things: (1) a knot sequ...