On the order of convergence of a determinantal family of root-finding methods

DOI10.1023/A:1022321325108zbMath0922.65037OpenAlexW1608551107MaRDI QIDQ1283250

Bahman Kalantari

Publication date: 13 April 1999

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022321325108

zbMATH Keywords

convergenceHalley's methodFibonacci numbersToeplitz matricesroot-finding iteration functionasymptotic error constantNetwon's methodupper Hessenberg matrices

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (11)

Inverse function, Taylor's expansion and extended Schröder's processes ⋮ Unnamed Item ⋮ Newton's method and generation of a determinantal family of iteration functions ⋮ On the rediscovery of Halley's iterative method for computing the zero of an analytic function ⋮ 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 ⋮ A computational comparison of the first nine members of a determinantal family of root-finding methods ⋮ Newton's method and high-order algorithms for the \(n\)th root computation ⋮ Higher order methods of the basic family of iterations via \(S\)-iteration scheme with \(s\)-convexity ⋮ Iterative root approximation in \(p\)-adic numerical analysis ⋮ An iteration method with maximal order based on standard information

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