Zeros of univariate interval polynomials

Authors:
Xuchuan Fan;Jiansong Deng;Falai Chen
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
Cited 2

A priori estimates for the zeros of interval polynomials

Journal of Computational and Applied Mathematics
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition

Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Comparison of interval methods for plotting algebraic curves

Computer Aided Geometric Design
On the computation of solutions of systems of interval polynomial equations

Journal of Computational and Applied Mathematics

Isolating the real roots of the piecewise algebraic variety

Computers & Mathematics with Applications
Number of zeros of interval polynomials

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros is exactly n if multiplicities are counted. The boundaries of complex block zeros on a complex plane are analyzed. Numeric algorithms to bound interval zeros and complex block zeros are presented.