A basic family of iteration functions for polynomial root finding and its characterizations

DOI10.1016/S0377-0427(97)00014-9zbMath0874.65037WikidataQ126572914 ScholiaQ126572914MaRDI QIDQ1360168

Iraj Kalantari, Rahim Zaare-Nahandi, Bahman Kalantari

Publication date: 10 November 1997

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

zbMATH Keywords

convergenceNewton's methodHalley's methodpolynomial root findingiteration formulas

Mathematics Subject Classification ID

Related Items (24)

On general convergence in extracting radicals via a fundamental family of iteration functions ⋮ On the convergence of Chebyshev's method for multiple polynomial zeros ⋮ On Schröder's families of root-finding methods ⋮ High order iterative methods for approximating square roots ⋮ On the convergence of Schröder's method for the simultaneous computation of polynomial zeros of unknown multiplicity ⋮ The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind ⋮ Algorithms for quaternion polynomial root-finding ⋮ The Padé iterations for the matrix sign function and their reciprocals are optimal ⋮ Recursive elucidation of polynomial congruences using root-finding numerical techniques ⋮ Polynomial and rational approximations and the link between Schröder's processes of the first and second kind ⋮ Newton's method and generation of a determinantal family of iteration functions ⋮ Symmetries of the Julia sets of König's methods for polynomials ⋮ On the rediscovery of Halley's iterative method for computing the zero of an analytic function ⋮ A combinatorial construction of high order algorithms for finding polynomial roots of known multiplicity ⋮ An infinite family of bounds on zeros of analytic functions and relationship to Smale’s bound ⋮ Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications ⋮ Characterization of the determinant of a Laguerre matrix ⋮ A computational comparison of the first nine members of a determinantal family of root-finding methods ⋮ Symmetric functions and root-finding algorithms ⋮ Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary ⋮ Iterative root approximation in \(p\)-adic numerical analysis ⋮ An iteration method with maximal order based on standard information ⋮ On rediscovered iteration methods for solving equations ⋮ On the convergence of Halley's method for multiple polynomial zeros

Cites Work

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• Computational complexity. On the geometry of polynomials and a theory of cost. I
• A family of one-point iteration formulae for finding roots
• On the Convergence of Halley's Method
• On Halley's Variation of Newton's Method
• Accelerated Convergence in Newton’s Method
• On the Geometry of Halley's Method
• On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equation
• A Type of Variation on Newton's Method
• The Solution of Equations by Continued Fractions

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