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ANALISIS ASUMSI METODE NEWTON RAPHSON DALAM MENGHAMPIRI SOLUSI PERSAMAAN NONLINEAR

Fitriah, Ana (2018) ANALISIS ASUMSI METODE NEWTON RAPHSON DALAM MENGHAMPIRI SOLUSI PERSAMAAN NONLINEAR. Undergraduate (S1) thesis, University of Muhammadiyah Malang.

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Abstract

The purpose of the study was to describe the impact if the Newton-Raphson method assumption was not fulfill. Based on what has happened to date that many people still use a method without knowing the assumptions that apply to the method. Thus, the user does not know what causes if there is obstacles when using the Newton-Raphson method to find the root of the nonlinear equation. This research uses direct and indirect proof to look for the impact that will occur if the assumptions are not fulfill. The assumptions used are two, f^' (x)≠0 and |(f(x_1)∙f"(x_1))/(f'(x_1)∙f'(x_1))|<1. The first assumption is f^' (x)≠0 uses indirect proof, while |(f(x_1)∙f"(x_1))/(f'(x_1)∙f'(x_1))|<1 uses direct proof. The result of the research is the solution is not found if f^' (x)≠0 is not fulfilled, because the root is almost at the extreme point if drawn using graph so the gradient is zero. If the initial estimate (x_0) does not satisfy |(f(x_1)∙f"(x_1))/(f'(x_1)∙f'(x_1))|<1 then the Newton-Raphson method will not convergent.

Item Type: Thesis (Undergraduate (S1))
Student ID: 201410060311175
Keywords: Nonlinear Equations, Equation Solutions, Equation Approximation, Newton-Raphson Methods, Assumptions, Newton-Raphson Method Assumptions, and Assumption Analysis.
Subjects: L Education > L Education (General)
Q Science > QA Mathematics
Divisions: Faculty of Teacher Training and Education > Department of Mathematics Education (84202)
Depositing User: CKO Repository
Date Deposited: 08 Nov 2018 07:25
Last Modified: 08 Nov 2018 07:25
URI : http://eprints.umm.ac.id/id/eprint/39643

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