Automatic Error bounds for Simple Zeros of Analytic Functions

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.

CACM February, 1973

Rokne, J.

real intervals, complex intervals, real interval
arithmetic, complex interval arithmetic, Newton's 
method, Cauchy-Ostrowski theorem, zeros of
polynomials, zeros of Bessel functions

5.11 5.12 5.15

CA730204 JB January 24, 1978  2:51 PM

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