# On Factorization of Analytic Functions and Its Verification

On Factorization of Analytic Functions and Its Verification An interval method for finding a polynomial factor of an analytic function f(z) is proposed. By using a Samelson-like method recursively, we obtain a sequence of polynomials that converges to a factor p*(z) of f(z) if an initial approximate factor p(z) is sufficiently close to p*(z). This method includes some well known iterative formulae, and has a close relation to a rational approximation. According to this factoring method, a fixed point relation for p*(z) is derived. Based on this relation, we obtain a polynomial with complex interval coefficients that includes p*(z). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# On Factorization of Analytic Functions and Its Verification

, Volume 6 (4) – Oct 16, 2004
12 pages
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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009931231719
Publisher site
See Article on Publisher Site

### Abstract

An interval method for finding a polynomial factor of an analytic function f(z) is proposed. By using a Samelson-like method recursively, we obtain a sequence of polynomials that converges to a factor p*(z) of f(z) if an initial approximate factor p(z) is sufficiently close to p*(z). This method includes some well known iterative formulae, and has a close relation to a rational approximation. According to this factoring method, a fixed point relation for p*(z) is derived. Based on this relation, we obtain a polynomial with complex interval coefficients that includes p*(z).

### Journal

Reliable ComputingSpringer Journals

Published: Oct 16, 2004

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