The newton’s method interval single-step procedure for bounding polynomial zeros simultaneously

Nuralif Akid Jamaludin, Mansor Monsi, Nasruddin Hassan

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The existing interval symmetric single-step procedure IMW established in 1988 has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton’s method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.

Original languageEnglish
Pages (from-to)241-252
Number of pages12
JournalFar East Journal of Mathematical Sciences
Volume97
Issue number2
DOIs
Publication statusPublished - 2015

Fingerprint

Polynomial Zeros
Newton Methods
Rate of Convergence
Interval
Iteration
Numerical Results

Keywords

  • CPU time
  • Interval analysis
  • Interval procedure
  • Simple zeros
  • Simultaneous inclusion

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The newton’s method interval single-step procedure for bounding polynomial zeros simultaneously. / Jamaludin, Nuralif Akid; Monsi, Mansor; Hassan, Nasruddin.

In: Far East Journal of Mathematical Sciences, Vol. 97, No. 2, 2015, p. 241-252.

Research output: Contribution to journalArticle

@article{8e8bba7d450044378ae45bab2b4bc6cc,
title = "The newton’s method interval single-step procedure for bounding polynomial zeros simultaneously",
abstract = "The existing interval symmetric single-step procedure IMW established in 1988 has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton’s method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.",
keywords = "CPU time, Interval analysis, Interval procedure, Simple zeros, Simultaneous inclusion",
author = "Jamaludin, {Nuralif Akid} and Mansor Monsi and Nasruddin Hassan",
year = "2015",
doi = "10.17654/FJMSMay2015_241_252",
language = "English",
volume = "97",
pages = "241--252",
journal = "Far East Journal of Mathematical Sciences",
issn = "0972-0871",
publisher = "University of Allahabad",
number = "2",

}

TY - JOUR

T1 - The newton’s method interval single-step procedure for bounding polynomial zeros simultaneously

AU - Jamaludin, Nuralif Akid

AU - Monsi, Mansor

AU - Hassan, Nasruddin

PY - 2015

Y1 - 2015

N2 - The existing interval symmetric single-step procedure IMW established in 1988 has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton’s method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.

AB - The existing interval symmetric single-step procedure IMW established in 1988 has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton’s method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.

KW - CPU time

KW - Interval analysis

KW - Interval procedure

KW - Simple zeros

KW - Simultaneous inclusion

UR - http://www.scopus.com/inward/record.url?scp=84929579272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929579272&partnerID=8YFLogxK

U2 - 10.17654/FJMSMay2015_241_252

DO - 10.17654/FJMSMay2015_241_252

M3 - Article

VL - 97

SP - 241

EP - 252

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 2

ER -