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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Computing the Brouwer degree in $R^{2}$
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by P. J. Erdelsky PDF
Math. Comp. 27 (1973), 133-137 Request permission

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
  • © Copyright 1973 American Mathematical Society
  • Journal: Math. Comp. 27 (1973), 133-137
  • MSC: Primary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1973-0326990-5
  • MathSciNet review: 0326990