94 citations · 144 across the 11 of their papers we have counts for
12 papers
A divided difference identity for a class of multiple integrals
Michael S. Floater
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral f…
Bounds on the determinant of an exponential matrix
Michael S. Floater
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
On the injectivity of mean value mappings between quadrilaterals
Michael S. Floater, Georg Muntingh
Mean value coordinates can be used to map one polygon into another, with application to computer graphics and curve and surface modelling. In this paper we show that if the polygon…
Best low-rank approximations and Kolmogorov n-widths
Michael S. Floater, Carla Manni, Espen Sande +1
We relate the problem of best low-rank approximation in the spectral norm for a matrix to Kolmogorov -widths and corresponding optimal spaces. We characterize all the optima…
On best constants in approximation
Andrea Bressan, Michael S. Floater, Espen Sande
In this paper we provide explicit upper and lower bounds on certain -widths, i.e., best constants in approximation. We further describe a numerical method to compute…
Transfinite mean value interpolation over polygons
Michael S. Floater, Francesco Patrizi
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in comp…
A characterization of supersmoothness of multivariate splines
Michael S. Floater, Kaibo Hu
We consider spline functions over simplicial meshes in $\RR^n$. We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are in…
Optimal spline spaces for -width problems with boundary conditions
Michael S. Floater, Espen Sande
In this paper we show that, with respect to the norm, three classes of functions in , defined by certain boundary conditions, admit optimal spline spaces of all deg…
Nodal bases for the serendipity family of finite elements
Michael S. Floater, Andrew Gillette
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the…
Gradient bounds for Wachspress coordinates on polytopes
Michael Floater, Andrew Gillette, N. Sukumar
We derive upper and lower bounds on the gradients of Wachspress coordinates defined over any simple convex d-dimensional polytope P. The bounds are in terms of a single geometric q…
Exact regularity of pseudo-splines
Michael S. Floater, Georg Muntingh
In this paper we review and refine a technique of Rioul to determine the Hölder regularity of a large class of symmetric subdivision schemes from the spectral radius of a single ma…
Divided Differences of Implicit Functions
Georg Muntingh, Michael S. Floater
Under general conditions, the equation implicitly defines locally as a function of . In this article, we express divided differences of in terms of bivariat…