Enclosing roots of polynomial equations and their applications to iterative processes

Enclosing roots of polynomial equations and their applications to iterative processes

We introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are...

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Bibliographic Details
Main Authors: Saïd Hilout, Ioannis K. Argyros
Format: Article
Language:English
Published: University Constantin Brancusi of Targu-Jiu 2009-11-01
Series:Surveys in Mathematics and its Applications
Subjects:
Real polynomials
Enclosing roots
Iterative processes
Nonlinear equations.
Online Access:http://www.utgjiu.ro/math/sma/v04/p10.pdf
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spelling doaj-b11d56d301ca465e9d6aca1e3e3da7102020-11-24T22:09:59ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982009-11-014 (2009)119132Enclosing roots of polynomial equations and their applications to iterative processesSaïd HiloutIoannis K. ArgyrosWe introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are expressed in closedform, and enclose all s<SUB>n</SUB> (n > 1). <BR>This technique is also used to find weaker than before[Kantorovich and Akilov, 1982] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.http://www.utgjiu.ro/math/sma/v04/p10.pdfReal polynomialsEnclosing rootsIterative processesNonlinear equations.
collection DOAJ
language English
format Article
sources DOAJ
author Saïd Hilout
Ioannis K. Argyros
spellingShingle Saïd Hilout
Ioannis K. Argyros
Enclosing roots of polynomial equations and their applications to iterative processes
Surveys in Mathematics and its Applications
Real polynomials
Enclosing roots
Iterative processes
Nonlinear equations.
author_facet Saïd Hilout
Ioannis K. Argyros
author_sort Saïd Hilout
title Enclosing roots of polynomial equations and their applications to iterative processes
title_short Enclosing roots of polynomial equations and their applications to iterative processes
title_full Enclosing roots of polynomial equations and their applications to iterative processes
title_fullStr Enclosing roots of polynomial equations and their applications to iterative processes
title_full_unstemmed Enclosing roots of polynomial equations and their applications to iterative processes
title_sort enclosing roots of polynomial equations and their applications to iterative processes
publisher University Constantin Brancusi of Targu-Jiu
series Surveys in Mathematics and its Applications
issn 1843-7265
1842-6298
publishDate 2009-11-01
description We introduce a special class of real recurrentpolynomials f<SUB>n</SUB> (n ≥ 1) of degree n,with unique positive roots s<SUB>n</SUB>, which are decreasingas n increases. The first root s<SUB>1</SUB>, as well asthe last one denoted by s<SUB>∞</SUB> are expressed in closedform, and enclose all s<SUB>n</SUB> (n > 1). <BR>This technique is also used to find weaker than before[Kantorovich and Akilov, 1982] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.
topic Real polynomials
Enclosing roots
Iterative processes
Nonlinear equations.
url http://www.utgjiu.ro/math/sma/v04/p10.pdf
work_keys_str_mv AT saidhilout enclosingrootsofpolynomialequationsandtheirapplicationstoiterativeprocesses
AT ioanniskargyros enclosingrootsofpolynomialequationsandtheirapplicationstoiterativeprocesses
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