A variable-dimension simplicial algorithm for antipodal fixed-point theorems
Michael J. Todd, Alden H. Wright · Numerical Functional Analysis and Optimization · 1980
Let and . The following is a version of the Borsuk-Ulam Theorem: If is continuous, and if for all , then there exists a y ε Bn such that f(y) = 0. Given ϵ > 0, we give a simplicial homotopy-type algorithm that will compute a point y such that . Unlike earlier simplicial algorithms for the Borsuk-Ulam problem, our method gives a computationally practical way of handling degeneracy. An application to the solution of systems of odd degree polynomials is given.