scholarly journals A High-Order Iterate Method for ComputingAT,S(2)

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoji Liu ◽  
Zemeng Zuo
Keyword(s):  
Iterative Method ◽  
Generalized Inverse ◽  
Higher Order ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Approximate Inverses

We investigate a new higher order iterative method for computing the generalized inverseAT,S(2)for a given matrixA. We also discuss how the new method could be applied for finding approximate inverses of nonsingular square matrices. Analysis of convergence is included to show that the proposed scheme has at least fifteenth-order convergence. Some tests are also presented to show the superiority of the new method.

scholarly journals A New High-Order Stable Numerical Method for Matrix Inversion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
F. Khaksar Haghani ◽  
F. Soleymani
Keyword(s):  
Iterative Method ◽  
Numerical Method ◽  
Matrix Inversion ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Initial Value ◽  
Numerical Examples ◽  
Stable Numerical Method

A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 260 ◽  
Author(s):  
Janak Sharma ◽  
Ioannis Argyros ◽  
Sunil Kumar
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Higher Order ◽  
High Order ◽  
Convergence Order ◽  
Eighth Order ◽  
First Derivative ◽  
Ball Convergence ◽  
Derivatives Of

The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since their convergence is not guaranteed. The convergence in this paper is shown, relying only on the first derivative. That is how we expand the applicability of some popular methods.

scholarly journals Some novel Newton-type methods for solving nonlinear equations

2019 ◽  
Vol 38 (3) ◽  
pp. 111-123
Author(s):  
Morteza Bisheh-Niasar ◽  
Abbas Saadatmandi
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Sixth Order ◽  
New Method ◽  
Order Convergence ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Newton Iterative Method

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature

scholarly journals Variations on Hermite Methods for Wave Propagation

2017 ◽  
Vol 22 (2) ◽  
pp. 303-337 ◽  
Author(s):  
Arturo Vargas ◽  
Jesse Chan ◽  
Thomas Hagstrom ◽  
Timothy Warburton
Keyword(s):  
Wave Propagation ◽  
Time Evolution ◽  
Discontinuous Galerkin ◽  
Hermite Interpolation ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Hyperbolic Pdes ◽  
High Order Convergence ◽  
Dg Methods

AbstractHermite methods, as introduced by Goodrich et al. in [15], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [4]. An example illustrates the simplification of this coupling for Hermite methods.

scholarly journals Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
F. Soleymani ◽  
M. Sharifi ◽  
S. Shateyi
Keyword(s):  
Iterative Method ◽  
Numerical Results ◽  
Order Convergence ◽  
Approximate Inverses ◽  
Square Matrix

This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence. The extension of the proposed iterative method for computing Moore-Penrose inverse is furnished. Numerical results including the comparisons with different existing methods of the same type in the literature will also be presented to manifest the superiority of the new algorithm in finding approximate inverses.

scholarly journals Convergence and Dynamics of a Higher-Order Method

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 420 ◽  
Author(s):  
Alejandro Moysi ◽  
Ioannis K. Argyros ◽  
Samundra Regmi ◽  
Daniel González ◽  
Á. Alberto Magreñán ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Higher Order ◽  
High Order ◽  
Local Form ◽  
Order Method ◽  
First Derivative ◽  
The Family ◽  
Higher Order Method

Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution. That is why, in this work, we analyze the convergence in a local form for an iterative method with a high order to find the solution of a nonlinear equation. We extend the applicability of previous results using only the first derivative that actually appears in the method. This is in contrast to either works using a derivative higher than one, or ones not in this method. Moreover, we consider the dynamics of some members of the family in order to see the existing differences between them.

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