How to increase convergence order of the Newton method to 2 × m ?

Sanjay Kumar Khattri

Applications of Mathematics (2014)

  • Volume: 59, Issue: 1, page 15-24
  • ISSN: 0862-7940

Abstract

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We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high precision, through the proposed scheme. Numerical work suggests that the presented scheme requires less number of function evaluations for convergence and it may be suitable in high precision computing.

How to cite

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Khattri, Sanjay Kumar. "How to increase convergence order of the Newton method to $2\times m$?." Applications of Mathematics 59.1 (2014): 15-24. <http://eudml.org/doc/260804>.

@article{Khattri2014,
abstract = {We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high precision, through the proposed scheme. Numerical work suggests that the presented scheme requires less number of function evaluations for convergence and it may be suitable in high precision computing.},
author = {Khattri, Sanjay Kumar},
journal = {Applications of Mathematics},
keywords = {iterative method; fourth order convergent method; eighth order convergent method; quadrature; Newton method; convergence; nonlinear equation; optimal choice; iterative method; fourth order convergent method; eighth order convergent method; quadrature; Newton method; nonlinear equation; optimal choice; numerical examples},
language = {eng},
number = {1},
pages = {15-24},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {How to increase convergence order of the Newton method to $2\times m$?},
url = {http://eudml.org/doc/260804},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Khattri, Sanjay Kumar
TI - How to increase convergence order of the Newton method to $2\times m$?
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 15
EP - 24
AB - We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high precision, through the proposed scheme. Numerical work suggests that the presented scheme requires less number of function evaluations for convergence and it may be suitable in high precision computing.
LA - eng
KW - iterative method; fourth order convergent method; eighth order convergent method; quadrature; Newton method; convergence; nonlinear equation; optimal choice; iterative method; fourth order convergent method; eighth order convergent method; quadrature; Newton method; nonlinear equation; optimal choice; numerical examples
UR - http://eudml.org/doc/260804
ER -

References

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