Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations

  • I.K. Argyros Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
  • D. Sharma Department of Mathematics, IIIT Bhubaneswar, Odisha, India
  • C.I. Argyros Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA
  • S.K. Parhi Department of Mathematics, Fakir Mohan University, Odisha 756020, India
  • S.K. Sunanda Department of Mathematics, IIIT Bhubaneswar, Odisha 751003, India
  • M.I. Argyros Department of Computer Science, Cameron University, Lawton, OK 73505, USA
Keywords: derivative free iterative algorithm;, order of convergence;, Banach space;, ball convergence

Abstract

In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth
order have been utilized to establish the convergence of a derivative free class of seventh order
iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were
given. In this study, extended ball convergence analysis is derived for this class by imposing
conditions on the first derivative. Additionally, we offer error distances and convergence radius
together with the region of uniqueness for the solution. Therefore, we enlarge the practical
utility of these algorithms. Also, convergence regions of a specific member of this class are displayed
for solving complex polynomial equations. At the end, standard numerical applications
are provided to illustrate the efficacy of our theoretical findings.

Author Biographies

I.K. Argyros, Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

D. Sharma, Department of Mathematics, IIIT Bhubaneswar, Odisha, India

Department of Mathematics, IIIT Bhubaneswar, Odisha, India

C.I. Argyros, Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA

Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA

S.K. Parhi, Department of Mathematics, Fakir Mohan University, Odisha 756020, India

Department of Mathematics, Fakir Mohan University, Odisha 756020, India

S.K. Sunanda, Department of Mathematics, IIIT Bhubaneswar, Odisha 751003, India

Department of Mathematics, IIIT Bhubaneswar, Odisha 751003, India

M.I. Argyros, Department of Computer Science, Cameron University, Lawton, OK 73505, USA

Department of Computer Science, Cameron University, Lawton, OK 73505, USA

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Published
2021-10-23
How to Cite
1.
Argyros I, Sharma D, Argyros C, Parhi S, Sunanda S, Argyros M. Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations. Mat. Stud. [Internet]. 2021Oct.23 [cited 2022Jan.20];56(1):72-. Available from: http://www.matstud.org.ua/ojs/index.php/matstud/article/view/228
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