Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets

DOI10.1137/S0036142997317365zbMath0928.30011WikidataQ123261313 ScholiaQ123261313MaRDI QIDQ4243569

Arno R. Bohm, N. Argyropoulos, Vassileios Drakopoulos

Publication date: 19 May 1999

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

iterationcritical pointJulia setFatou setSchröder's method

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Software, source code, etc. for problems pertaining to functions of a complex variable (30-04)

Related Items (11)

Dynamics of a family of third-order iterative methods that do not require using second derivatives ⋮ Are there any Julia sets for the Laguerre iteration function? ⋮ Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots ⋮ Repellers for the Laguerre Iteration Function ⋮ Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton's maps ⋮ The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind ⋮ On the global convergence of Schröder's iteration formula for real zeros of entire functions ⋮ Schröder iteration functions associated with a one-parameter family of biquadratic polynomials ⋮ On the global convergence of Schröder's iterative formulae for real roots of algebraic equations ⋮ Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary ⋮ HOW IS THE DYNAMICS OF KÖNIG ITERATION FUNCTIONS AFFECTED BY THEIR ADDITIONAL FIXED POINTS?

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