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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.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-142-84
Published Here
February 23, 2012