Computer tools for the construction and analysis of some efficient root-finding simultaneous methods

Analysis of algorithms (68W40) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical computation of solutions to single equations (65H05) Numerical approximation and evaluation of special functions (33F05)

Uses Software

na10

Cites Work

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Numerical computation of polynomial zeros by means of Aberth's method
Graphic and numerical comparison between iterative methods
Iteration functions re-visited
On an application of symbolic computation and computer graphics to root-finders: the case of multiple roots of unknown multiplicity
Numerical methods for roots of polynomials. Part I
Relationships between different types of initial conditions for simultaneous root finding methods
Point estimation of root finding methods
General local convergence theory for a class of iterative processes and its applications to Newton's method
A note on some improvements of the simultaneous methods for determination of polynomial zeros
Locating multiple zeros interactively
Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
On the global convergence of Halley's iteration formula
On rediscovered iteration methods for solving equations
Dynamic study of Schröder's families of first and second kind
Symbolic computation and computer graphics as tools for developing and studying new root-finding methods
Unified convergence analysis for Picard iteration in \(n\)-dimensional vector spaces
Iterative methods for simultaneous inclusion of polynomial zeros
Numerical methods for roots of polynomials. II
On the global convergence of Schröder's iteration formula for real zeros of entire functions
Computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros
On iteration methods without derivatives for the simultaneous determination of polynomial zeros
On Schröder's families of root-finding methods
New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
An algorithm for the total, or partial, factorization of a polynomial
Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
A note on \(Q\)-order of convergence
General convergence theorems for iterative processes and applications to the Weierstrass root-finding method

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