Automatic errorbounds for simple zeros of analytic functions

Authors:
J. Rokne
Affiliations:
Univ. of Calgary, Calgary, Alberta, Canada
Venue:
Communications of the ACM
Year:
1973

Citing 4
Cited 1

Complex interval arithmetic

Communications of the ACM
A stopping criterion for polynomial root finding

Communications of the ACM
Algorithm 61: procedures for range arithmetic

Communications of the ACM
Rounding Errors in Algebraic Processes

Rounding Errors in Algebraic Processes

Enclosing all zeros of an analytic function - A rigorous approach

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	48.22

Visualization

Abstract

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.