Computational geometry as a tool for studying root-finding methods

DOI10.2298/FIL1904019PzbMath1499.65176OpenAlexW2998341741MaRDI QIDQ5080708

Ivan Petković, Lidija Z. Rančić

Publication date: 31 May 2022

Published in: Filomat (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/fil1904019p

zbMATH Keywords

basin of attractioncomputational geometrygraphic visualizationdynamic studyparametric iterative methods

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical computation of solutions to single equations (65H05) Complexity and performance of numerical algorithms (65Y20) Numerical approximation and evaluation of special functions (33F05)

Related Items (3)

Iterative schemes for finding all roots simultaneously of nonlinear equations ⋮ A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography ⋮ Computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros

Uses Software

• Mathematica

Cites Work

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• Graphic and numerical comparison between iterative methods
• Iteration functions re-visited
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Symbolic computation and computer graphics as tools for developing and studying new root-finding methods
• Basins of attraction for several optimal fourth order methods for multiple roots

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