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).
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Sakurai, T., Sugiura, H. On Factorization of Analytic Functions and Its Verification. Reliable Computing 6, 459–470 (2000). https://doi.org/10.1023/A:1009931231719
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DOI: https://doi.org/10.1023/A:1009931231719