Numerical computation of polynomial zeros by means of Aberth's method

DOI10.1007/BF02207694zbMath0869.65034OpenAlexW2043237762WikidataQ61908527 ScholiaQ61908527MaRDI QIDQ676928

Dario Andrea Bini

Publication date: 1 September 1997

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02207694

zbMATH Keywords

algorithmHorner schemeLaguerre methodroots of a polynomialWilkinson polynomial

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05) Real polynomials: location of zeros (26C10)

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Cites Work

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• Simple algorithms for approximating all roots of a polynomial with real roots
• Inclusion of the roots of a polynomial based on Gerschgorin's theorem
• Initial approximations in Durand-Kerner's root finding method
• Sequential and parallel complexity of approximate evaluation of polynomial zeros
• A comparison of methods for terminating polynomial iterations
• A bibliography on roots of polynomials
• Some remarks on Dvorcuk's root-finding method
• A posteriori error bounds for the zeros of polynomials
• A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration
• Generalizations of an algorithm of Sebastião e Silva
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• Circular arithmetic and the determination of polynomial zeros
• A posteriori error bounds for the zeros of a polynomial
• Simultaneous inclusion of the zeros of a polynomial
• A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem
• The Durand-Kerner polynomials roots-finding method in case of multiple roots
• A Machine Method for Solving Polynomial Equations
• A Termination Criterion for Iterative Methods Used to Find the Zeros of Polynomials
• A Globally Convergent Method for Simultaneously Finding Polynomial Roots
• Root Neighborhoods of a Polynomial
• The fundamental theorem of algebra and complexity theory
• Calculation of Zeros of a Real Polynomial Through Factorization Using Euclid’s Algorithm
• Some modifications of Laguerre's method
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
• On the Convergence Speed of Some Algorithms for the Simultaneous Approximation of Polynomial Roots
• A modified Newton method for polynomials
• A stopping criterion for polynomial root finding
• On the Convergence of Sebastião E. Silva’s Method for Finding a Zero of a Polynomial
• Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
• Practical Problems Arising in the Solution of Polynomial Equations
• On a theorem by J. L. Walsh concerning the moduli of roots of algebraic equations