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Scaled parallel iterative method for finding real roots of nonlinear equations

Given a nonconvex minimization problem where the objective function is nonlinear and twice differentiable. To gain more information about the objective function, it is essential to obtain all its stationary points and study the behaviour of these points. Since many nonlinear functions are expressibl...

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Main Authors: Chen, Chuei Yee, Ghazali, Abdul Hakim, Leong, Wah June
Format: Article
Published: Informa UK Limited 2021
Online Access:http://psasir.upm.edu.my/id/eprint/103136/
https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1873985
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spelling my.upm.eprints.1031362024-11-25T02:53:39Z http://psasir.upm.edu.my/id/eprint/103136/ Scaled parallel iterative method for finding real roots of nonlinear equations Chen, Chuei Yee Ghazali, Abdul Hakim Leong, Wah June Given a nonconvex minimization problem where the objective function is nonlinear and twice differentiable. To gain more information about the objective function, it is essential to obtain all its stationary points and study the behaviour of these points. Since many nonlinear functions are expressible as polynomials via interpolation, there is a need to devise fast and accurate algorithms in finding root(s) of the interpolating polynomial. Through interval computation, the Weierstrass-like parallel iterative methods are known for their efficiency in finding polynomial zeros. However, these schemes are highly dependent on the midpoints of each interval in generating successive intervals. In this study, we propose a scaling function on some Weierstrass-like parallel iterative methods such that the procedures are less dependent on the generated midpoints, hence allowing a more efficient search for the zeros while reducing the width of the intervals. The proposed procedures with the shifted centres of the enclosing intervals are tested on 120 problems and we compare their efficiency with the existing Weierstrass-like methods in terms of the number of iterations and largest final interval width. The results indicate that the proposed procedures outperform the original procedures, giving more reduction on the final interval width with a lesser number of iterations. Informa UK Limited 2021 Article PeerReviewed Chen, Chuei Yee and Ghazali, Abdul Hakim and Leong, Wah June (2021) Scaled parallel iterative method for finding real roots of nonlinear equations. Optimization, 71 (9). pp. 2595-2611. ISSN 0233-1934; eISSN: 1029-4945 https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1873985 10.1080/02331934.2021.1873985
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description Given a nonconvex minimization problem where the objective function is nonlinear and twice differentiable. To gain more information about the objective function, it is essential to obtain all its stationary points and study the behaviour of these points. Since many nonlinear functions are expressible as polynomials via interpolation, there is a need to devise fast and accurate algorithms in finding root(s) of the interpolating polynomial. Through interval computation, the Weierstrass-like parallel iterative methods are known for their efficiency in finding polynomial zeros. However, these schemes are highly dependent on the midpoints of each interval in generating successive intervals. In this study, we propose a scaling function on some Weierstrass-like parallel iterative methods such that the procedures are less dependent on the generated midpoints, hence allowing a more efficient search for the zeros while reducing the width of the intervals. The proposed procedures with the shifted centres of the enclosing intervals are tested on 120 problems and we compare their efficiency with the existing Weierstrass-like methods in terms of the number of iterations and largest final interval width. The results indicate that the proposed procedures outperform the original procedures, giving more reduction on the final interval width with a lesser number of iterations.
format Article
author Chen, Chuei Yee
Ghazali, Abdul Hakim
Leong, Wah June
spellingShingle Chen, Chuei Yee
Ghazali, Abdul Hakim
Leong, Wah June
Scaled parallel iterative method for finding real roots of nonlinear equations
author_facet Chen, Chuei Yee
Ghazali, Abdul Hakim
Leong, Wah June
author_sort Chen, Chuei Yee
title Scaled parallel iterative method for finding real roots of nonlinear equations
title_short Scaled parallel iterative method for finding real roots of nonlinear equations
title_full Scaled parallel iterative method for finding real roots of nonlinear equations
title_fullStr Scaled parallel iterative method for finding real roots of nonlinear equations
title_full_unstemmed Scaled parallel iterative method for finding real roots of nonlinear equations
title_sort scaled parallel iterative method for finding real roots of nonlinear equations
publisher Informa UK Limited
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/103136/
https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1873985
_version_ 1817844591769944064
score 13.244413

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