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

DOI:
https://doi.org/10.1090/S0025-5718-1978-0492046-9

MathSciNet review:
492046

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0492046-9

Keywords:
Brouwer Fixed Point Theorem,
constructive proof,
Transversality theorem,
degree theory,
vector fields on spheres

Article copyright:
© Copyright 1978
American Mathematical Society