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All Journal Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam
M. Imran
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Mathematics

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ANALISIS KEKONVERGENAN GLOBAL METODE ITERASI CHEBYSHEV Poppy Hanggreny; M. Imran; Zulkarnain '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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Abstract

This article discusses the analysis of the global convergence of Chebyshev method through the geometric interpretation of how to derive its formula using the parabolic equation. The results of the analysis are posed in the theorems, which state hypotheses criteria when the Chebyshev method converges globally for any initial guess at some intervals. For comparison, the hypotheses criteria when the Euler method and Halley iteration convergen globally are also discussed. In comparing these methods through the computations, we look into the fulfillment of the hypotheses criteria of the theorems for each method and the number of iterations required to obtain the estimated roots.
FORMULASI UMUM METODE ITERASI DENGAN ORDE KONVERGENSI ENAM Dewi Khairati Putri; M. Imran; Zulkarnain '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

This article discusses the General Formulation of Iterative Method, which requires three function evaluations and one derivative function evaluation. Analytically it is showed, using the Taylor expansion and geometric series, that the General Formulation of Iterative Method has a convergence of order six. Furthermore, by choosing the values of certain parameters in the General Formulation of Iterative Method, several well-known iterative methods, which have three function evaluations and one derivative function evaluation, are obtained. Comparison between the proposed method and well-known methods are done by looking at the number of iterations and number of function evaluation. In addition, comparisons are also made through Basins of Attraction of the methods discussed.
Co-Authors Dewi Khairati Putri Poppy Hanggreny Zulkarnain '