ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS

Shams M., Rafiq N., Kausar N., Agarwal P., Mir N. A., Li Y.

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, vol.30, no.10, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 10
  • Publication Date: 2022
  • Doi Number: 10.1142/s0218348x22401983
  • Journal Name: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Multiple Roots, Iterative Technique, Convergence Order, Computational Efficiency, CPU-Time, SIMULTANEOUS APPROXIMATION, ITERATIVE METHODS, CONVERGENCE, ZEROS, ORDER, FORMULA, FAMILY
  • Yıldız Technical University Affiliated: Yes

Abstract

This paper develops optimal family of fourth-order iterative techniques in order to find a single root and to generalize them for simultaneous finding of all roots of polynomial equation. Convergence study reveals that for single root finding methods, its optimal convergence order is 4, while for simultaneous methods, it is 12. Computational cost and numerical illustrations demonstrate that the newly developed family of methods outperformed the previous methods available in the literature.