Finding zeroes of maps: homotopy methods that are constructive with probability one 论文

摘要

We illustrate that most existence theorems using degree theory are in principle relatively constructive. The first one presented here is the Brouwer Fixed Point Theorem. Our method is "constructive with probability one" and can be implemented by computer. Other existence theorems are also proved by the same method. The approach is based on a transversality theorem.