Zur numerischen Bestimmung des Abbildungsgrades im ${\mathbb{R}}^n$ I

Abstract

Two formulas computing the topological degree of a continuous function $\Phi$ relative to an $n$-dimensional polyhedron $P^n$ are presented. Both formulas are based on the same idea of construction. Let T be a triangulation of the boundary of $P^n$ and let f$(c)$ = sgn $\Phi (e),e\in$ E(T), be a simplicial mapping from T into a boundary triangulation of the $n$-dimensional unit cube, then the topological degree of the function $\Phi$ relative to $P^n$ is given by

if T is oriented in a suitable manner.

The second computation formula is based on a simplicial mapping from T into the natural boundary triangulation of the $n$-dimensional unit octahedron.