Global aspects of the continuous and discrete Newton method: A case study

DOI10.1007/BF00047504zbMath0669.65038OpenAlexW4239862943MaRDI QIDQ1118980

Klaus Schmitt, Heinz-Otto Peitgen, Michael Pruefer

Publication date: 1988

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00047504

zbMATH Keywords

convergencecomplex polynomialsbifurcationphase portraitssingular setdamped Newton methodfractal basin boundarycomputer graphic diagramscontinuous Newton's methodJulia set theoryNewton flow

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Dynamics induced by flows and semiflows (37C10) Length, area, volume, other geometric measure theory (28A75) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

An acceleration of the continuous Newton's method, CONJECTURES ABOUT SIMPLE DYNAMICS FOR SOME REAL NEWTON MAPS ON ℝ2, Dynamics of Newton Maps of Quadratic Polynomial Maps of ℝ2 into Itself, Finding all periodic orbits of maps using Newton methods: Sizes of basins, Adaptive cellular integration of linearly implicit differential equations, Stability of singular equilibria in quasilinear implicit differential equations, Continuous Newton's method for polynomials., On an application of dynamical systems theory to determine all the zeros of a vector function, Weak singularities and the continuous Newton method, Discretization of implicit ODEs for singular root-finding problems

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