Point estimation of simultaneous methods for solving polynomial equations: A survey

DOI10.1016/S0377-0427(00)00620-8zbMath1002.65058OpenAlexW4205364252MaRDI QIDQ5948584

Miodrag S. Petković, Đorđe D. Herceg

Publication date: 20 December 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00620-8

zbMATH Keywords

convergenceiterative methodspolynomial equationspoint estimationpolynomial zerossimple zerosinitial conditions for convergence

Mathematics Subject Classification ID

Related Items (17)

On the guaranteed convergence of the fourth order simultaneous method for polynomial zeros ⋮ A feasible implementation procedure for interval analysis method from measurement data ⋮ On a cubically convergent derivative-free root finding method ⋮ On the convergence of the sequences of Gerschgorin-like disks ⋮ On a modification of the Ehrlich–Aberth method for simultaneous approximation of polynomial zeros ⋮ On the guaranteed convergence of the square-root iteration method ⋮ The guaranteed convergence of Laguerre-like method ⋮ A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously ⋮ Relationships between different types of initial conditions for simultaneous root finding methods ⋮ A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously ⋮ A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods ⋮ Chebyshev-like root-finding methods with accelerated convergence ⋮ Improved algorithms for computing determinants and resultants ⋮ The convergence of a family of parallel zero-finding methods ⋮ A new fourth-order family of simultaneous methods for finding polynomial zeros ⋮ General convergence theorems for iterative processes and applications to the Weierstrass root-finding method ⋮ 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A parallel algorithm for simple roots of polynomials
• On dominating sequence method in the point estimate and Smale's theorem
• On zero finding methods of higher order from data at one point
• A family of simultaneous zero-finding methods
• An iteration formula for the simultaneous determination of the zeros of a polynomial
• A family of root finding methods
• Safe convergence of simultaneous methods for polynomial zeros
• On the convergence of Wang-Zheng's method
• Improvement of a convergence condition for Durand-Kerner iteration
• Weierstrass formula and zero-finding methods
• Point estimation and some applications to iterative methods
• Point estimation of a family of simultaneous zero-finding methods
• The theory of Smale's point estimation and its applications
• On some methods for the simultaneous determination of polynomial zeros
• On initial conditions for the convergence of simultaneous root finding methods
• On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials
• A posteriori error bounds for the zeros of polynomials
• Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• Zur iterativen Auflösung algebraischer Gleichungen
• Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II
• On Approximate Zeros and Rootfinding Algorithms for a Complex Polynomial
• On the efficiency of algorithms of analysis
• Computational complexity. On the geometry of polynomials and a theory of cost. I
• The fundamental theorem of algebra and complexity theory
• Convergence and Complexity of Newton Iteration for Operator Equations
• Convergence of Newton’s method and inverse function theorem in Banach space
• Approximate Zeros of Quadratically Convergent Algorithms
• Börsch-supan-like methods: point estimation and parallel implementation
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• A modified Newton method for polynomials
• A Note on the Convergence of Newton’s Method

This page was built for publication: Point estimation of simultaneous methods for solving polynomial equations: A survey