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The Computer Journal 1964 7(3):212-219; doi:10.1093/comjnl/7.3.212
© 1964 by British Computer Society
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A combined graphical and iterative approach to the problem of finding zeros of functions in the complex plane

F. M. Larkin *

U.K.A.E.A. Research Group, Culham Laboratory, Abingdon, UK

The paper describes how an automatic graph plotter, used as a digital computer output device, is capable of providing useful regional and global information about functions in the complex plane. This information, in the form of the approximate locations and types of zeros, singularities and branch cuts, enables one to choose starting points for zero finding iterations with a high degree of confidence in their convergence. A number of contour graphs are presented which illustrate general features of complex functions near typical zeros, poles and essential singularities.


* U.K.A.E.A. Research Group, Culham Laboratory, Nr. Abingdon, Berks.


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