Yuslenita Muda
Department of Mathematics, Faculty of Science and Technology, State Islamic University of Sultan Syarif Kasim Riau

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TRACE OF THE ADJACENCY MATRIX n×n OF THE CYCLE GRAPH TO THE POWER OF TWO TO FIVE Fitri Aryani; Dian Ayu Puspita; Corry Corazon Marzuki; Yuslenita Muda
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (548.147 KB) | DOI: 10.30598/barekengvol16iss2pp393-408

Abstract

The main aim of this research is to find the formula of the trace of adjacency matrix from a cycle graph to the power of two to five. To obtain the general form, the first step is finding the general formula of the adjacency matrix from a cycle graph to the power of two to five. Furthermore, the formula of the trace of adjacency matrix which is mentioned above obtained and proven by direct proof. We also present an implementation of the formula which is given by an example.
SOME MODIFICATIONS OF CHEBYSHEV-HALLEY’S METHODS FREE FROM SECOND DERIVATIVE WITH EIGHTH-ORDER OF CONVERGENCE Yuslenita Muda; Neng Santi; Wartono Wartono; Muhafzan Muhafzan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (501.493 KB) | DOI: 10.30598/barekengvol16iss2pp531-538

Abstract

The variant of Chebyshev-Halley’s method is an iterative method used for solving a nonlinear equation with third order of convergence. In this paper, we present some new variants of three steps Chebyshev-Halley’s method free from second derivative with two parameters. The proposed methods have eighth-order of convergence for and and require four evaluations of functions per iteration with index efficiency equal to . Numerical simulation will be presented by using several functions to show the performance of the proposed methods.