Computing the Brouwer degree in

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 , a generalization of the zero-counting integral , for functions which are Lipschitz continuous on a piecewise linear path of integration, using only computed or observed values of , 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.

**[1]**L. M. Delves and J. N. Lyness,*A numerical method for locating the zeros of an analytic function*, Math. Comp.**21**(1967), 543–560. MR**0228165**, 10.1090/S0025-5718-1967-0228165-4**[2]**James Dugundji,*Topology*, Allyn and Bacon, Inc., Boston, Mass., 1966. MR**0193606****[3]**Peter Henrici and Irene Gargantini,*Uniformly convergent algorithms for the simultaneous approximation of all zeros of a polynomial*, Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967) Wiley-Interscience, New York, 1969, pp. 77–113. MR**0256553****[4]**G. W. Stewart III,*Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division*, Math. Comp.**25**(1971), 135–139. MR**0292333**, 10.1090/S0025-5718-1971-0292333-7

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0326990-5

Keywords:
Brouwer degree,
zeros of functions

Article copyright:
© Copyright 1973
American Mathematical Society