Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method

Deepak Kumar, Janak Raj Sharma and Lorentz Jäntschi
Additional contact information
Deepak Kumar: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India
Janak Raj Sharma: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania

Mathematics, 2019, vol. 7, issue 10, 1-11

Abstract: To locate a locally-unique solution of a nonlinear equation, the local convergence analysis of a derivative-free fifth order method is studied in Banach space. This approach provides radius of convergence and error bounds under the hypotheses based on the first Fréchet-derivative only. Such estimates are not introduced in the earlier procedures employing Taylor’s expansion of higher derivatives that may not exist or may be expensive to compute. The convergence domain of the method is also shown by a visual approach, namely basins of attraction. Theoretical results are endorsed via numerical experiments that show the cases where earlier results cannot be applicable.

Keywords: local convergence; nonlinear equations; Banach space; Fréchet-derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/10/919/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/10/919/ (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:7:y:2019:i:10:p:919-:d:273090

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 ().