Metode Iterasi Dua Titik Berparameter Real dengan orde Konvergensi Optimal

Authors

  • Wartono Wartono Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia
  • Ika Safitri Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia

DOI:

https://doi.org/10.15575/kubik.v5i2.6037

Keywords:

Indeks efisiensi, metode iterasi dua titik, orde konvergensi, persamaan nonlinier

Abstract

Pada artikel ini, sebuah metode iterasi baru dikonstruksi menggunakan generalisasi metode iterasi dua titik dengan delapan parameter real A, B, C, D, E, F, G, dan H. Generalisasi bentuk metode iterasi dilakukan untuk menentukan orde konvergensi optimal dengan mengganti nilai-nilai parameter real. Hasil kajian menunjukkan bahwa metode iterasi mempunyai orde konvergensi tiga yang melibatkan delapan parameter real. Selanjutnya orde konvergensi metode iterasi meningkat dengan mengganti  A = E dan B = F + 2  sehingga hanya melibatkan enam parameter real. Selain itu, metode iterasi memerlukan  tiga evaluasi fungsi dan memiliki indeks efisiensi sebesar 41/3 » 1,5874. Simulasi numerik diberikan untuk menguji performasi metode baru dengan menggunakan beberapa fungsi real. Performa metode iterasi baru tersebut adalah jumlah iterasi, orde konvergensi yang dihitung secara komputasi dan nilai mutlak fungsi. Selanjutnya, ukuran-ukuran performasi metode iterasi baru dibandingkan dengan Metode Newton, Metode Chun, Metode Newton Ganda dan Metode Noor. Hasil simulasi numerik menunjukkan bahwa metode iterasi baru mempunyai performa lebih baik dibandingkan dengan metode iterasi lainnya

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Published

2020-11-10

How to Cite

Wartono, W., & Safitri, I. (2020). Metode Iterasi Dua Titik Berparameter Real dengan orde Konvergensi Optimal. KUBIK: Jurnal Publikasi Ilmiah Matematika, 5(2), 118–128. https://doi.org/10.15575/kubik.v5i2.6037

Issue

Vol. 5 No. 2 (2020): KUBIK: Jurnal Publikasi Ilmiah Matematika

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