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 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.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

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 Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 138
Author(s):  
Alyaa A. Al-Qarni ◽  
Huda O. Bakodah ◽  
Aisha A. Alshaery ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Numerical Results ◽  
Decomposition Algorithm ◽  
Adomian Decomposition ◽  
High Level ◽  
Do So

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.

An optimum iterative method for solving any linear system with a square matrix

1988 ◽  
Vol 28 (1) ◽  
pp. 163-178 ◽  
Author(s):  
Dennis C. Smolarski ◽  
Paul E. Saylor
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Square Matrix

Three-Step Method with Fifth-Order Convergence for Nonlinear Equation

2013 ◽  
Vol 846-847 ◽  
pp. 1274-1277
Author(s):  
Ying Peng Zhang ◽  
Li Sun
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Efficiency Index ◽  
Newton Methods ◽  
Order Convergence ◽  
Step Method ◽  
Second Derivatives ◽  
Fifth Order ◽  
Modified Newton Methods ◽  
Better Than

We present a fifth-order iterative method for the solution of nonlinear equation. The new method is based on two ordinary methods, which are modified Newton methods without second derivatives. Its efficiency index is 1.37973 which is better than that of Newton's method. Numerical results show the efficiency of the proposed method.

scholarly journals Analysis of a New Fractional Model for Damped Bergers’ Equation

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Fractional Model ◽  
Applied Method ◽  
The Stability

AbstractIn this article, we present a fractional model of the damped Bergers’ equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.

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 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

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