Gauss-Steiner Continuization
Han de Bruijn
The definition of Gauss-Steiner Continuization, as employed in this
article, is the following. A set of discrete real function values is
the range of values to be approximated, with a function that is
continuous and differentiable. This is to be accomplished with a comb
of Gauss distributions. Therefore we start with a generalization of
one-dimensional Uniform Combs of Gaussians, for irregular 1-D grids
and non-constant functions. The two-dimensional discretization has an
arbitrary Finite Element like mesh of triangles as its domain.
With help of our family of Steiner ellipses, an analogue of the one-
dimensional comb of Gauss distributions is constructed.
The discretization at hand is made continuous and differentiable in
this way. Prerequisite reading is the article "Steiner Ellipses and
Variances" at:
http://hdebruijn.soo.dto.tudelft.nl/jaar2011/steiners.pdf . Posting:
http://groups.google.com/group/sci.math/msg/00f32e12d1103373?hl=en
Han de Bruijn
Han de Bruijn
There is an update of the article and accompanying (free) software:
http://hdebruijn.soo.dto.tudelft.nl/jaar2011/gauss_2d.pdf
http://hdebruijn.soo.dto.tudelft.nl/jaar2011/steiners.zip
Han de Bruijn