scholarly journals A New Iterative Method for Finding Approximate Inverses of Complex Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
M. Kafaei Razavi ◽  
A. Kerayechian ◽  
M. Gachpazan ◽  
S. Shateyi
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Complex Matrices ◽  
Approximate Inverse ◽  
Numerical Examples ◽  
Convergence Behavior ◽  
Approximate Inverses ◽  
Nonsingular Matrices ◽  
New Iterative Method

This paper presents a new iterative method for computing the approximate inverse of nonsingular matrices. The analytical discussion of the method is included to demonstrate its convergence behavior. As a matter of fact, it is proven that the suggested scheme possesses tenth order of convergence. Finally, its performance is illustrated by numerical examples on different matrices.

scholarly journals A New Sixth Order Method for Nonlinear Equations inR

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Sukhjit Singh ◽  
D. K. Gupta
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Performance Measure ◽  
Sixth Order ◽  
Order Method ◽  
Numerical Examples ◽  
Real Roots ◽  
New Iterative Method ◽  
Number Of Iterations

A new iterative method is described for finding the real roots of nonlinear equations inR. Starting with a suitably chosenx0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered.

scholarly journals A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fiza Zafar ◽  
Gulshan Bibi
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Numerical Examples ◽  
New Class ◽  
First Derivative ◽  
New Methods ◽  
Specific Step

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

scholarly journals On the simultaneous improving k inclusion disks for polynomial zeros

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 9-21
Author(s):  
Dusan Milosevic ◽  
Miodrag Petkovic
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Convergence Properties ◽  
Polynomial Zeros ◽  
Numerical Examples ◽  
Modified Method

A modification of the iterative method of B?rsch-Supan type for the simultaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of k (of n ? k) zeros, dealing with k inclusion disks of these zeros and the point (unchangeable) approximations to the remaining n - k zeros. It is proved that the R-order of convergence of the considered method is two if k < n and three if k = n. Three numerical examples are given to illustrate convergence properties of the presented method. .

scholarly journals On the fourth order zero-finding methods for polynomials

Filomat ◽  
2003 ◽  
pp. 35-46
Author(s):  
Snezana Ilic ◽  
Lidija Rancic
Keyword(s):  
Fourth Order ◽  
Order Of Convergence ◽  
Simultaneous Approximation ◽  
New Method ◽  
Main Attention ◽  
Simple Complex ◽  
Order Zero ◽  
Numerical Examples ◽  
Convergence Behavior ◽  
Complex Zeros

The fourth order methods for the simultaneous approximation of simple complex zeros of a polynomial are considered. The main attention is devoted to a new method that may be regarded as a modification of the well known cubically convergent Ehrlich-Aberth method. It is proved that this method has the order of convergence equals four. Two numerical examples are given to demonstrate the convergence behavior of the studied methods.

scholarly journals New Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 11 (4) ◽  
pp. 1649-1654 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
New Method ◽  
New Iterative Method

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

scholarly journals A New Iterative Method for Linear Systems from XFEM

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jianping Zhao ◽  
Yanren Hou ◽  
Haibiao Zheng ◽  
Bo Tang
Keyword(s):  
Finite Element Method ◽  
Iterative Method ◽  
Model Problem ◽  
Linear Equations ◽  
Governing Equations ◽  
Numerical Examples ◽  
Cpu Time ◽  
Whole Process ◽  
Linear Elastostatics ◽  
New Iterative Method

The extend finite element method (XFEM) is popular in structural mechanics when dealing with the problem of the cracked domains. XFEM ends up with a linear system. However, XFEM usually leads to nonsymmetric and ill-conditioned stiff matrix. In this paper, we take the linear elastostatics governing equations as the model problem. We propose a new iterative method to solve the linear equations. Here we separate two variablesUand Enr, so that we change the problems into solving the smaller scale equations iteratively. The new program can be easily applied. Finally, numerical examples show that the proposed method is more efficient than common methods; we compare theL2-error and the CPU time in whole process. Furthermore, the new XFEM can be applied and optimized in many other problems.

scholarly journals A New Variant of Newton’s Method With Fourth–Order Convergence

2016 ◽  
Vol 21 (1) ◽  
pp. 86-89
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Method ◽  
Linear Combination ◽  
Newton Method ◽  
Fourth Order ◽  
Inverse Function ◽  
Order Convergence ◽  
Numerical Examples ◽  
New Variant ◽  
Indefinite Integral ◽  
New Iterative Method

In this paper, we present new iterative method for solving nonlinear equations with fourth-order convergence. This method is free from second and higher order derivatives. We find this iterative method by using Newton's theorem for inverse function and approximating the indefinite integral in Newton's theorem by the linear combination of harmonic mean rule and Wang formula. Numerical examples show that the new method competes with Newton method, Weerakoon - Fernando method and Wang method.Journal of Institute of Science and TechnologyVol. 21, No. 1, 2016, page :86-89

scholarly journals Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1329-1346
Author(s):  
Caiqin Song ◽  
Qing-Wen Wang
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Matrix Equation ◽  
Inner Product ◽  
Frobenius Norm ◽  
Finite Convergence ◽  
Numerical Examples ◽  
Roundoff Errors ◽  
New Iterative Method

By introducing the real inner product, this paper offers an modified conjugate gradient least squares iterative algorithm (MCGLS)for solving the generalized Sylvester-conjugate matrix equation. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This new iterative method can obtain the symmetric least squares Frobenius norm solution within finite iteration steps in the absence of roundoff errors. Finally, two numerical examples are offered to illustrate the effectiveness of the proposed algorithm.

scholarly journals Analyzing a New Third Order Iterative Method for Solving Nonlinear Problems

2021 ◽  
pp. 72-90
Author(s):  
M. S. Ndayawo ◽  
B. Sani
Keyword(s):  
Iterative Method ◽  
Series Expansion ◽  
Nonlinear Problems ◽  
Third Order ◽  
Numerical Examples ◽  
Adomian Method ◽  
The Individual ◽  
New Iterative Method ◽  
Number Of Iterations ◽  
Taylor’S Series

In this paper, we propose and analyse a new iterative method for solving nonlinear equations. The method is constructed by applying Adomian method to Taylor’s series expansion. Using one-way analysis of variance (ANOVA), the method is being compared with other existing methods in terms of the number of iterations and solution to convergence between the individual methods used. Numerical examples are used in the comparison to justify the efficiency of the new iterative method.

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