On the order of convergence of a determinantal family of root-finding methods
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Publication:1283250
DOI10.1023/A:1022321325108zbMath0922.65037OpenAlexW1608551107MaRDI QIDQ1283250
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
convergenceHalley's methodFibonacci numbersToeplitz matricesroot-finding iteration functionasymptotic error constantNetwon's methodupper Hessenberg matrices
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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