An algorithm for numerical calculation of topological degree

Abstract

Let be a continuous function from a connected n-dimensional polyhedron Pn to Rn. Assume Φn does not vanish on the boundary b(Pn) so that the topological degree of Φn relative to the origin is defined. Let ω_i be the modulus of continuity of Assume where the Ω_n are known functions which are O(t). An algorithm is given which subdivides b(P_n) in a certain way, then terminates; the degree may then be readily calculated using a formula of[6] in a special way which avoids much of the computation.