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Sains Malaysiana 49(7)(2020): 1755-1764
http://dx.doi.org/10.17576/jsm-2020-4907-25
Suatu Kelas Kaedah Optimum Bak Steffensen Bebas Terbitan untuk Punca
Berganda
SYAHMI AFANDI SARIMAN & ISHAK HASHIM*
Jabatan
Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600
UKM Bangi, Selangor Darul Ehsan, Malaysia
Diserahkan: 24 Mac 2020/Diterima: 10 April 2020
ABSTRAK
Objektif utama makalah ini adalah untuk mencari punca berganda bagi
persamaan tak linear. Kaedah lelaran tiga tahap diubah suai menjadi bebas
terbitan yang mengekalkan peringkat penumpuan optimum lapan. Skema lelaran
bebas terbitan dibangunkan berdasarkan kaedah bak Steffensen dan konsep beza terhingga.
Kaedah yang diubah suai ini selaras dengan penumpuan optimum mengikut konjektur
Kung Traub yang dibuktikan melalui analisis penumpuan. Skema lelaran ini dapat
bersaing dengan kaedah lelaran sedia ada daripada segi kebebasan terbitan.
Indeks keberkesanan telah mencapai nilai
Kata kunci: Bebas terbitan; kaedah lelaran; penumpuan optimum; persamaan
tak linear; punca berganda
ABSTRACT
The main objective of this paper was to find multiple roots for
nonlinear equations. The three-step iteration method is modified to be
derivative free which maintains an optimum convergence of eight. The
derivative-free iteration scheme was developed based on the Steffensen-like
method and finite difference concept. The modified method satisfies the optimal
convergence of Kung-Traub’s conjectures as shown in the convergence analysis.
The iteration scheme can compete with the existing iteration methods in terms
of free derivatives. The efficiency index has reached the value
Keywords:
Derivative-free; iterative method; multiple roots; nonlinear equation; optimal
convergence
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*Pengarang untuk
surat-menyurat; email: ishak_h@ukm.edu.my
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