SIMPLIFICATION OF STENGER TOPOLOGICAL DEGREE FORMULA

A formula due to F. Stenger expresses the topological degree of a continuous mapping defined on a polyhedron in Rn as a constant times a sum of determinants of n×n matrices. We replace these determinant evaluations by a scanning procedure which examines their associated matrices and at each of n-1 steps discards at least half of the matrices remaining from the previous step. Finally we obtain a lower bound for the number of matrices present originally, thus giving an estimate for the minimum amount of labour needed in many cases to compute the degree using this method. © 1979 Springer-Verlag.