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Automatic errorbounds for simple zeros of analytic functions

By J. Rokne

Communications of the ACM, Vol. 16 No. 2, Pages 101-104

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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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