One-Point Optimal Family of Multiple Root Solvers of Second-Order

Deepak Kumar, Janak Raj Sharma and Clemente Cesarano
Additional contact information
Deepak Kumar: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
Janak Raj Sharma: Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
Clemente Cesarano: Section of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

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

Abstract: This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure of weight functions. The convergence behavior is discussed by showing some essential conditions of the weight function. The well-known modified Newton method is a member of the proposed family for particular choices of the weight function. The dynamical nature of different members is presented by using a technique called the “basin of attraction”. Several practical problems are given to compare different methods of the presented family.

Keywords: nonlinear equations; multiple roots; one-point methods; optimal convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/7/655/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/7/655/ (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:7:p:655-:d:250370

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 ().