scholarly journals Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

2021 ◽  
Vol 11 (2) ◽  
pp. 6-11
Author(s):  
Dr. Roopa K M ◽  
◽  
Venkatesha P ◽  
Keyword(s):  
Numerical Methods ◽  
Comparative Study ◽  
Iterative Methods ◽  
Numerical Comparison ◽  
Polynomial Equations ◽  
Chebyshev Method ◽  
Newton Raphson ◽  
Raphson Method ◽  
Iterative Numerical Methods

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

scholarly journals Fractional Newton–Raphson Method Accelerated with Aitken’s Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 47
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz ◽  
U. Iturrarán-Viveros ◽  
R. Caballero-Cruz
Keyword(s):  
Fractional Derivative ◽  
Iterative Methods ◽  
Fractional Integral ◽  
Order Of Convergence ◽  
Fractional Operators ◽  
Speed Of Convergence ◽  
Newton Raphson ◽  
Raphson Method

In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB

2017 ◽  
Vol 1 (1) ◽  
pp. 95
Author(s):  
Siti Nurhabibah Hutagalung
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Abstract - The study of the characteristics of non-liier functions can be carried out experimentally and theoretically. One part of theoretical analysis is computation. For computational purposes, numerical methods can be used to solve equations complicated, for example non-linear equations. There are a number of numerical methods that can be used to solve nonlinear equations, the Newton-Raphson method. Keywords - Numerical, Newton Raphson.

scholarly journals Inverse Multiscale Discrete Radon Transform by Filtered Backprojection

2020 ◽  
Vol 11 (1) ◽  
pp. 22
Author(s):  
José G. Marichal-Hernández ◽  
Ricardo Oliva-García ◽  
Óscar Gómez-Cárdenes ◽  
Iván Rodríguez-Méndez ◽  
José M. Rodríguez-Ramos
Keyword(s):  
Numerical Methods ◽  
Inverse Problems ◽  
Iterative Methods ◽  
Radon Transform ◽  
Discrete Version ◽  
Filtered Backprojection ◽  
Discrete Radon Transform ◽  
First Time ◽  
The Sacrifice ◽  
Iterative Numerical Methods

The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.

scholarly journals PEMBUATAN APLIKASI PEMBELAJARAN PENCARIAN AKAR PERSAMAAN

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Amanda A. Diadema ◽  
Gunawan Santosa ◽  
Nugroho Agus Haryono
Keyword(s):  
Fixed Point ◽  
Numerical Methods ◽  
Undergraduate Students ◽  
The Other ◽  
Root Yield ◽  
Minimal Action ◽  
Newton Raphson ◽  
Learning Software ◽  
Raphson Method

In numerical methods, finding the root of an equation involves iterations to find an estimated root approximating the original root. Several methods that can be used to find the root are Fixed-Point Iteration Method, Newton-Raphson Method, Secant Method and the Muller Method. This learning software is developed to provide a learning media for students to learn how to find the root of an equation. It contains animated explanation of the study material, case study and exercises. The software then tested to users using Usability Test, namely compatibility, consistency, flexibility, learnability, perceptual limitation, and minimal action. Tests performed to undergraduate students who have learned how to find equation root yield these results: Compatibility 86.13%, Consistency 83.73%, Flexibility 84.23%, Learnability 81.87%, Minimal Action 84.80%, and Perceptual Limitation 85.07%. On the other hand, tests performed to undergraduate students who have never learned how to find equation root yield these results: Compatibility 85.33%, Consistency 86.67%, Flexibility 83.47%, Learnability 85.87%, Minimal Action 87.20%, and Perceptual Limitation 82.67%.

The solution of algebraic equations on the EDSAC

1952 ◽  
Vol 48 (2) ◽  
pp. 255-270 ◽  
Author(s):  
R. A. Brooker
Keyword(s):  
Iterative Methods ◽  
Algebraic Equations ◽  
Newton Raphson ◽  
Raphson Method

AbstractThis paper is an account of the methods that have been used with the EDSAC for the solution of algebraic equations. Three repetitive or iterative methods are examined: Bernoulli's method, the root-squaring method, and the Newton-Raphson method. Experience with the EDSAC has shown that, as in hand computing, quadratically convergent methods are to be preferred to those less rapidly convergent. In particular, the Newton-Raphson method has proved the most useful. Several examples are given in the appendix.

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