On the convergence condition of generalized root iterations for the inclusion of polynomial zeros
DOI10.1016/j.matcom.2007.05.002zbMath1146.65044OpenAlexW2005454998MaRDI QIDQ929751
Dušan M. Milošević, Miodrag S. Petković
Publication date: 18 June 2008
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matcom.2007.05.002
polynomial zerosinterval methodscomplex zerosalgebraic polynomialscircular interval arithmeticconvergence conditionsinclusion methodscircular complex arithmeticsimultaneous inclusion
Interval and finite arithmetic (65G30) 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)
Uses Software
Cites Work
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- Ostrowski-like method with corrections for the inclusion of polynomial zeros
- A computational test for the existence of a polynomial zero
- On zero finding methods of higher order from data at one point
- On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
- On an iterative method for simultaneous inclusion of polynomial complex zeros
- Parallel Laguerre iterations: The complex case
- Weierstrass formula and zero-finding methods
- Ten methods to bound multiple roots of polynomials
- Design, analysis, and implementation of a multiprecision polynomial rootfinder
- Iterative methods for simultaneous inclusion of polynomial zeros
- The theory of Smale's point estimation and its applications
- Optimal and nearly optimal algorithms for approximating polynomial zeros
- A higher order family for the simultaneous inclusion of multiple zeros of polynomials
- Circular arithmetic and the determination of polynomial zeros
- On the convergent condition of Newton-like method in parallel circular iteration for simultaneously finding all multiple zeros of a polynomial. II
- On Approximate Zeros and Rootfinding Algorithms for a Complex Polynomial
- A Note on the Evaluation in Circular Arithmetics
- An Existence Test for Root Clusters and Multiple Roots
- On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros
- Further Applications of Circular Arithmetic: Schroeder-Like Algorithms with Error Bounds for Finding Zeros of Polynomials
- Approximate Zeros of Quadratically Convergent Algorithms
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