On some methods for the simultaneous determination of polynomial zeros

DOI10.1007/BF03167248zbMath0859.65047OpenAlexW2001799574MaRDI QIDQ1922231

Tetsuro Yamamoto, Nikolay Kyurkchiev, Sachio Kanno

Publication date: 7 April 1997

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167248

zbMATH Keywords

convergencenumerical exampleszeros of polynomialsWeierstrass methodDurand-Kerner methodsimultaneous iterative methodsSOR-like acceleration

Mathematics Subject Classification ID

Related Items (28)

ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS ⋮ ON INVERSE ITERATION PROCESS FOR FINDING ALL ROOTS OF NONLINEAR EQUATIONS WITH APPLICATIONS ⋮ Scaled parallel iterative method for finding real roots of nonlinear equations ⋮ The behaviour of approximations of the SOR Weierstrass method ⋮ A note on the convergence of the Weierstrass SOR method for polynomial roots ⋮ On nonlinear SOR-like methods. I: Applications to simultaneous methods for polynomial zeros ⋮ Efficient optimal eighth-order derivative-free methods for nonlinear equations ⋮ A note on the Le Verrier-Fadeev's method ⋮ On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously ⋮ On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation ⋮ Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation ⋮ On a modification of the Ehrlich–Aberth method for simultaneous approximation of polynomial zeros ⋮ On Euler-like methods for the simultaneous approximation of polynomial zeros ⋮ Point estimation and some applications to iterative methods ⋮ Convergence of the two-point Weierstrass root-finding method ⋮ Local and semilocal convergence of a family of multi-point Weierstrass-type root-finding methods ⋮ ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS ⋮ Study of dynamical behavior and stability of iterative methods for nonlinear equation with applications in engineering ⋮ Some families of two-step simultaneous methods for determining zeros of nonlinear equations ⋮ A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods ⋮ Inverse numerical iterative technique for finding all roots of nonlinear equations with engineering applications ⋮ On new higher order families of simultaneous methods for finding polynomial zeros ⋮ An efficient higher order family of root finders ⋮ On a generalization of the Euler-Chebyshev method for simultaneous extraction of only a part of all roots of polynomials ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey ⋮ Computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros ⋮ Global Convergence Properties of the SOR-Weierstrass Method ⋮ On dynamics of iterative techniques for nonlinear equation with applications in engineering

Cites Work

• Balanced convergence of iterative methods to a multiple zero of a complex polynomial
• A posteriori error bounds for the zeros of polynomials
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• The Durand-Kerner polynomials roots-finding method in case of multiple roots
• An improvement on two iteration methods for simultaneous determination of the zeros of a polynomial
• 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
• Certain modifications of Newton's method for the approximate solution of algebraic equations
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