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Mathematics of Computation

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

Authors: Shui Nee Chow, John Mallet-Paret and James A. Yorke
Journal: Math. Comp. 32 (1978), 887-899
MSC: Primary 55M25; Secondary 47H10, 65H10, 90C99
MathSciNet review: 492046
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Abstract: 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.

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Keywords: Brouwer Fixed Point Theorem, constructive proof, Transversality theorem, degree theory, vector fields on spheres
Article copyright: © Copyright 1978 American Mathematical Society