1984 Reports

Can We Approximate Zeros of Functions with Non-zero Topological Degree?

Boult, Terrance E.; Sikorski, Krzysztof A.

The bisection method provides an affirmative answer for scalar functions. We show that the answer is negative for bivariate functions. This means, in particular, that an arbitrary continuation method cannot approximate a zero of every smooth bivariate function with non-zero topological degree.