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Home/Magazine Archive/February 1973 (Vol. 16, No. 2)/Automatic errorbounds for simple zeros of analytic.../Abstract

Automatic errorbounds for simple zeros of analytic functions

By J. Rokne
Communications of the ACM, February 1973, Vol. 16 No. 2, Pages 101-104
10.1145/361952.361962
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The Cauchy-Ostrowski theorem on convergence of Newton iterates for an analytic function in one variable is extended to include computational errors using complex interval arithmetic. Several numerical examples are given for polynomials with real and complex roots and one example for the Bessel function of the first kind.

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