A family of root-finding methods with accelerated convergence

DOI10.1016/j.camwa.2005.10.013zbMath1134.65347OpenAlexW2053153056MaRDI QIDQ2475888

Miodrag S. Petković, Lidija Z. Rančić

Publication date: 11 March 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2005.10.013

zbMATH Keywords

convergence analysisnumerical examplesiterative methodsNewton methodGauss-Seidel methodcomplex zerosaccelerated convergence\(R\)-order of convergenceHalley's correctionssimultaneous iterative methodsdetermination of polynomial zeros

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) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05)

Related Items (4)

Bounds for the zeros of complex-coefficient polynomials ⋮ An efficient higher order family of root finders ⋮ Iteration functions re-visited ⋮ The polynomial pivots as initial values for a new root-finding iterative method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new higher-order family of inclusion zero-finding methods
• The guaranteed convergence of Laguerre-like method
• Asynchronous polynomial zero-finding algorithms
• Finding the roots of a polynomial on an MIMD multicomputer
• Some modifications of the parallel Halley iteration method and their convergence
• On Euler-like methods for the simultaneous approximation of polynomial zeros
• On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
• Parallel Laguerre iterations: The complex case
• Enclosing clusters of zeros of polynomials
• Ten methods to bound multiple roots of polynomials
• A method for finding the zeros of polynomials using a companion matrix.
• A new fourth-order family of simultaneous methods for finding polynomial zeros
• Iterative methods for simultaneous inclusion of polynomial zeros
• Optimal and nearly optimal algorithms for approximating polynomial zeros
• Computing the zeros of analytic functions
• A higher order family for the simultaneous inclusion of multiple zeros of polynomials
• Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• Circular arithmetic and the determination of polynomial zeros
• The fundamental theorem of algebra and complexity theory
• 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

This page was built for publication: A family of root-finding methods with accelerated convergence