A Practical Method of Numerical Calculation of the Mapping Degree

Abstract

This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : n → n at a regular value 0 relative to a bounded open subset B ⊂ n. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n + 1 operations using interval arithmetic.