Proving the existence of zeros using the topological degree and interval arithmetic

摘要

The invariance of the topological degree under certain homotopies is used to computationally prove the existence of zeros of nonlinear mappings in Rn. These existence tests use interval arithmetic to enclose the range of a function over a box. We show that our test is more general than a well-known test based on Miranda's theorem, and we show by a numerical example that the new test can be successful on substantially larger boxes.