A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously

DOI10.1007/s11075-016-0237-1zbMath1375.65065OpenAlexW2556940223MaRDI QIDQ2407926

Stoil I. Ivanov

Publication date: 6 October 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0237-1

zbMATH Keywords

iterative algorithmerror estimatesnumerical examplessemilocal convergencelocation of zerospolynomial zerossimultaneous methodsnormed fields

Mathematics Subject Classification ID

Related Items (6)

ON INVERSE ITERATION PROCESS FOR FINDING ALL ROOTS OF NONLINEAR EQUATIONS WITH APPLICATIONS ⋮ Local and semilocal convergence of a family of multi-point Weierstrass-type root-finding methods ⋮ Convergence analysis of Sakurai-Torii-Sugiura iterative method for simultaneous approximation of polynomial zeros ⋮ On the convergence of Schröder's method for the simultaneous computation of polynomial zeros of unknown multiplicity ⋮ Unified convergence analysis for Picard iteration in \(n\)-dimensional vector spaces ⋮ On the local convergence of Gargantini-Farmer-Loizou method for simultaneous approximation of multiple polynomial zeros

Cites Work

• Unnamed Item
• Unnamed Item
• On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously
• Semilocal convergence of Chebyshev-like root-finding method for simultaneous approximation of polynomial zeros
• On the local convergence of Ehrlich method for numerical computation of polynomial zeros
• Convergence of the two-point Weierstrass root-finding method
• On a family of Weierstrass-type root-finding methods with accelerated convergence
• On the convergence of Halley's method for simultaneous computation of polynomial zeros
• Relationships between different types of initial conditions for simultaneous root finding methods
• General local convergence theory for a class of iterative processes and its applications to Newton's method
• Safe convergence of simultaneous methods for polynomial zeros
• Weierstrass formula and zero-finding methods
• A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods
• A unified theory of cone metric spaces and its applications to the fixed point theory
• On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials
• Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
• Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros
• A new semilocal convergence theorem for the Weierstrass method from data at one point
• A modified Newton method for polynomials
• Certain modifications of Newton's method for the approximate solution of algebraic equations
• A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic
• Point estimation of simultaneous methods for solving polynomial equations: A survey
• General convergence theorems for iterative processes and applications to the Weierstrass root-finding method

This page was built for publication: A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously