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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing the Brouwer degree in $ R\sp{2}$


Author: P. J. Erdelsky
Journal: Math. Comp. 27 (1973), 133-137
MSC: Primary 65D20
MathSciNet review: 0326990
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Abstract: A very simple rigorous procedure is derived for computing the Brouwer degree in $ {R^2}$, a generalization of the zero-counting integral $ \oint {f'(z)\;dz/f(z)} $, for functions which are Lipschitz continuous on a piecewise linear path of integration, using only computed or observed values of $ f(z)$, a bound for the error in them, and a bound for the Lipschitz constant. It is used to locate zeros and to test the numerical significance of zeros found by other methods.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0326990-5
PII: S 0025-5718(1973)0326990-5
Keywords: Brouwer degree, zeros of functions
Article copyright: © Copyright 1973 American Mathematical Society