Extending the Applicability of a Two-Step Vectorial Method with Accelerators of Order Five for Solving Systems of Equations

Ioannis K. Argyros, Stepan Shakhno, Yurii Shunkin, Samundra Regmi () and Nirjal Shrestha
Additional contact information
Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Stepan Shakhno: Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Universytetska Str. 1, 79000 Lviv, Ukraine
Yurii Shunkin: Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Universytetska Str. 1, 79000 Lviv, Ukraine
Samundra Regmi: Department of Mathematics, University of Houston, Houston, TX 77205, USA
Nirjal Shrestha: Department of Mathematics, University of Florida, Gainesville, FL 32603, USA

Mathematics, 2025, vol. 13, issue 8, 1-19

Abstract: The local convergence analysis of a two-step vectorial method of accelerators with order five has been shown previously. But the convergence order five is obtained using Taylor series and assumptions on the existence of at least the fifth derivative of the mapping involved, which is not present in the method. These assumptions limit the applicability of the method. Moreover, a priori error estimates or the radius of convergence or uniqueness of the solution results have not been given. All these concerns are addressed in this paper. Furthermore, the more challenging semi-local convergence analysis, not previously studied, is presented using majorizing sequences. The convergence for both analyses depends on the generalized continuity of the Jacobian of the mapping involved, which is used to control it and sharpen the error distances. Numerical examples validate the sufficient convergence conditions presented in the theory.

Keywords: two-step vectorial method with accelerators; convergence; order five (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/8/1299/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/8/1299/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:8:p:1299-:d:1635352

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().