One-Point Optimal Family of Multiple Root Solvers of Second-Order
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 fu...
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doaj-70bbb0b79b44403e91ce89c7df540b312020-11-25T01:42:51ZengMDPI AGMathematics2227-73902019-07-017765510.3390/math7070655math7070655One-Point Optimal Family of Multiple Root Solvers of Second-OrderDeepak Kumar0Janak Raj Sharma1Clemente Cesarano2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, IndiaSection of Mathematics, International Telematic University UNINETTUNO, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyThis 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.https://www.mdpi.com/2227-7390/7/7/655nonlinear equationsmultiple rootsone-point methodsoptimal convergence |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Deepak Kumar Janak Raj Sharma Clemente Cesarano |
spellingShingle |
Deepak Kumar Janak Raj Sharma Clemente Cesarano One-Point Optimal Family of Multiple Root Solvers of Second-Order Mathematics nonlinear equations multiple roots one-point methods optimal convergence |
author_facet |
Deepak Kumar Janak Raj Sharma Clemente Cesarano |
author_sort |
Deepak Kumar |
title |
One-Point Optimal Family of Multiple Root Solvers of Second-Order |
title_short |
One-Point Optimal Family of Multiple Root Solvers of Second-Order |
title_full |
One-Point Optimal Family of Multiple Root Solvers of Second-Order |
title_fullStr |
One-Point Optimal Family of Multiple Root Solvers of Second-Order |
title_full_unstemmed |
One-Point Optimal Family of Multiple Root Solvers of Second-Order |
title_sort |
one-point optimal family of multiple root solvers of second-order |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2019-07-01 |
description |
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. |
topic |
nonlinear equations multiple roots one-point methods optimal convergence |
url |
https://www.mdpi.com/2227-7390/7/7/655 |
work_keys_str_mv |
AT deepakkumar onepointoptimalfamilyofmultiplerootsolversofsecondorder AT janakrajsharma onepointoptimalfamilyofmultiplerootsolversofsecondorder AT clementecesarano onepointoptimalfamilyofmultiplerootsolversofsecondorder |
_version_ |
1725034729961422848 |