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Indexed by:期刊论文

Date of Publication:2011-11-25

Journal:THEORETICAL COMPUTER SCIENCE

Included Journals:Scopus、SCIE、EI

Volume:412

Issue:50

Page Number:7029-7043

ISSN No.:0304-3975

Key Words:Nearest polynomial; Zero; Complex; Perturbation; I(infinity)-norm

Abstract:Given a univariate complex polynomial f and a closed complex domain D, whose boundary C is a curve parameterized by a piecewise rational function, we propose two computational algorithms for finding a univariate complex polynomial (f) over tilde such that (f) over tilde has a zero in D and the distance between f and (f) over tilde is minimal. Our approach is composed of two steps. First, in the case of D consisting of one point alpha, we give explicit formulas of (f) over tilde and the minimal distance in terms of alpha. Next, the case of a general closed domain D is considered by using the property that a nearest polynomial (f) over tilde has a zero on the boundary C. The curve C is parameterized piecewisely, and on each piece we search for the minimum of the distance between f and (f) over tilde. At this step we exploit the explicit formula of the minimal distance as a function of a point alpha. Then the global minimum and the nearest polynomial are obtained by comparing the piecewise minima. Some examples are presented: one of them confirms that the distance between a nearest complex polynomial and a given polynomial is less than that between a nearest real polynomial and the given polynomial. (C) 2011 Elsevier B.V. All rights reserved.