The MULTIPLISITAS NEWTON DAN TITIK TETAP ATRAKTIF DALAM MENENTUKAN KEKONVERGENAN

  • Gani Gunawan FMIPA UNISBA
Keywords: Multiplicity, Newton's Method

Abstract

Abstract. Newton's method is one of the numerical methods used in finding polynomial roots. This method will be very effective to use, if the initial estimate of the roots for the Newton iteration function satisfies sufficient Newtonian convergence, [11]. In this article we will analyze the efficacy of this method by looking at the relationship between the fixed point method and Newton's iteration function. When the iteration of the function converges to the root, the velocity of convergence can also be determined. In terms of the speed of convergence, it turns out to be very dependent on the multiplicity of Newton's method itself.

  

 

References

DAFTAR PUSTAKA
[1] Capra, Steven C and Canale, Raymond P, Numerical Methods for Engineers with Personal Computer Applications, MacGraw-Hill Book Company, 1991.
[2] Elis R Wulan, Sri M Sukarti, Diny Zulkarnaen, Perbandingan Tingkat Kecepatan Konvergensi dari Metoda Newton Raphson dan Metoda Secant Setelah Mengaplikasi Metoda Aiken’s dalam Perhitungan akar Pangkat Tiga, Jurnal Matematika Integratif, Volume 12 No. 1, April 2016. Pp 35-42
[3] Epperson. F James, An Introductions to Numerical Methods and Analysis, John Wiley & Sons, Inc, USA, 2001.
[4] Fink, Kurtis. D, Numerical Methods Using Matlab 3rd Edition, Prentice Hall, Inc. USA. 1999.
[5] Mahmul, Mariatul Kitfiah, Yudhi, Modifikasi Metode Newton-Raphson Untuk Mencari Solusi Persamaan Linier dan Non Linier, Buletin Ilmiah Mat.Stat, dan Terapannya (Bimaster) Volume 6 No.02, 2017, hal 69-76
[6] Mathew, John. H, Numerical Methods for Mathematics, Science and Engineering, 2nd Editioni, Prentice-Hall International, USA, 1993.
[7] Patrisius Batarius, Nilai Awal Pada Metode Newton-Raphson yang Dimodifikasi dalam Penentuan Akar Persamaan, Pi: Mathematics Education Journal, Volume 1. No.3 Oktober 2018, 105-112
[8] Raskin, S, Newton’s Method, Research Report, 2006.
[9] Zaytman, Genya, “Newton’s Method”, Research Report, 2005.
[10] Zuhnia Lega, Agusni, Supriadi Putra, Metoda Iterasi Tiga Langkah Dengan Orde Konvergensi Lima Untuk Menyelesaikan Persamaan Non Linier Berakar Ganda, JOM FMIPA Volume 1 No. 2, Oktober 2014
Published
2020-12-23
How to Cite
Gunawan, G. (2020). The MULTIPLISITAS NEWTON DAN TITIK TETAP ATRAKTIF DALAM MENENTUKAN KEKONVERGENAN. Jurnal Ilmiah Matrik, 22(3), 333–338. https://doi.org/10.33557/jurnalmatrik.v22i3.1107
Section
Articles
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