Approximate Zeros of Quadratically Convergent Algorithms

DOI10.2307/2153572zbMath0814.65044OpenAlexW2007951771MaRDI QIDQ4305971

Pengyuan Chen

Publication date: 15 September 1994

Full work available at URL: https://doi.org/10.2307/2153572

zbMATH Keywords

complexityiterative algorithmNewton's methodefficiencyquadratic convergencezeros of holomorphic functions

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) Complexity and performance of numerical algorithms (65Y20)

Related Items (22)

Uniform convergence of higher order quasi Hermite-Fejér interpolation ⋮ Two-square theorems for infinite matrices on certain fields ⋮ Extended Newton methods for conic inequalities: approximate solutions and the extended Smale \(\alpha\)-theory ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey. II. ⋮ On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces ⋮ On the guaranteed convergence of the square-root iteration method ⋮ The guaranteed convergence of Laguerre-like method ⋮ Local convergence of the Newton’s method in two step nilpotent Lie groups ⋮ Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions ⋮ Local and global behavior for algorithms of solving equations ⋮ On the convergence condition of generalized root iterations for the inclusion of polynomial zeros ⋮ Newton's method for sections on Riemannian manifolds: Generalized covariant \(\alpha \)-theory ⋮ The convergence of a family of parallel zero-finding methods ⋮ A new fourth-order family of simultaneous methods for finding polynomial zeros ⋮ Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition ⋮ Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey ⋮ Local convergence of Newton's method on the Heisenberg group ⋮ On the guaranteed convergence of new two-point root-finding methods for polynomial zeros ⋮ Point estimation of a family of simultaneous zero-finding methods ⋮ On the convergence of Wang-Zheng's method ⋮ Convergence of Newton’s method and inverse function theorem in Banach space

Cites Work

• On a theorem of S. Smale about Newton's method for analytic mappings
• On zero finding methods of higher order from data at one point
• 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

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