Continuous Newton's method for polynomials.

DOI10.1007/BF03025411zbMath1052.30502MaRDI QIDQ5949231

John W. Neuberger

Publication date: 18 November 2001

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (15)

Adaptive Newton-type schemes based on projections ⋮ An acceleration of the continuous Newton's method ⋮ Global existence of real roots and random Newton flow algorithm for nonlinear system of equations ⋮ ON THE DYNAMICS OF SOME NUMERICAL METHODS ⋮ Numerical properties of different root-finding algorithms obtained for approximating continuous Newton's method ⋮ The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives ⋮ THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS ⋮ Graphic and numerical comparison between iterative methods ⋮ An adaptive Newton-method based on a dynamical systems approach ⋮ A global Newton-type scheme based on a simplified Newton-type approach ⋮ Newton flow of the Riemann zeta function: separatrices control the appearance of zeros ⋮ The order completion method for systems of nonlinear PDEs revisited ⋮ Newton Method and Trajectory-Based Method for Solving Power Flow Problems: Nonlinear Studies ⋮ Prospects for a central theory of partial differential equations ⋮ Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

Cites Work

• Unnamed Item
• The continuous, desingularized Newton method for meromorphic functions
• Discrete versus continuous Newton's method: A case study
• Global aspects of the continuous and discrete Newton method: A case study
• Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
• Sobolev gradients and differential equations

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