Voronoi diagram properties in polynomials with polynomiography applications and extensions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We have previously established delicate connections between the Voronoi diagram of polynomial roots and their basins of attraction with respect to the Basic Family of iteration functions. We have also previously defined polynomiography, visualization techniques in solving a polynomial equation, resulting in a medium with multidisciplinary applications. Here we describe several novel results and survey our recent work on polynomials and polynomiography and their extensions and applications. These include, (i) extension of root-finding methods to analytic functions and the analysis of infinite Voronoi diagram and basins of attraction of their roots; (ii) an application of polynomiography in the visualization of least square polynomial approximations; (iii) a Voronoi diagram property of roots of a cubic equation in connection to its critical points and its algorithmic application; (iv) association of polynomiography to special matrices such as permutation matrices, Latin Squares and Sudoku solutions, and alternating sign matrices. We will consider the application of the above and present corresponding polynomiographies.

Original languageEnglish (US)
Title of host publicationProceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012
Pages32-40
Number of pages9
DOIs
StatePublished - 2012
Event2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012 - Piscataway, NJ, United States
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012

Other

Other2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012
Country/TerritoryUnited States
CityPiscataway, NJ
Period6/27/126/29/12

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Basins of attraction
  • Complex polynomials
  • Dynamical systems
  • Iteration functions
  • Newton's method
  • Voronoi diagrams
  • Zeros

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