American Journal of Numerical Analysis
ISSN (Print): 2372-2118 ISSN (Online): 2372-2126 Website: http://www.sciepub.com/journal/ajna Editor-in-chief: Emanuele Galligani
Open Access
Journal Browser
Go
American Journal of Numerical Analysis. 2014, 2(3), 76-78
DOI: 10.12691/ajna-2-3-2
Open AccessEditorial

A Discussion on the Practicability of an Analytical Method for Solving System of Linear Equations

H. Saberi Najafi1, S.A. Edalatpanah1, and N. Vosoughi1

1Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Pub. Date: March 23, 2014

Cite this paper:
H. Saberi Najafi, S.A. Edalatpanah and N. Vosoughi. A Discussion on the Practicability of an Analytical Method for Solving System of Linear Equations. American Journal of Numerical Analysis. 2014; 2(3):76-78. doi: 10.12691/ajna-2-3-2

Abstract

Unfailing real world problems in engineering, economics, finance, etc. can lead to solving a system of linear equations. In this paper we give a survey a new approach to solve this problem based on homotopy perturbation method. Furthermore, we show that the solving linear equations by using a new method called modified homotopy perturbation method, presented in [M.A. Noor, K.I. Noor, S. Khan, M. Waseem, Modified homotopy perturbation method for solving system of linear equations. Journal of the Association of Arab Universities for Basic and Applied Sciences., 13(2013)35-37] is impractical.

Keywords:
linear system exact solution auxiliary matrix initial value arbitrary operator

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  D. M. Young, Iterative solution of large linear systems, Academic Press, New York, 1971.
 
[2]  A. Berman, R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic, New York, 1994.
 
[3]  R.S. Varga, Matrix iterative analysis, second ed., Springer, Berlin, 2000.
 
[4]  H. Saberi Najafi, S. A. Edalatpanah, Comparison analysis for improving preconditioned SOR-type iterative Method, Numerical Analysis and Applications., 6(2013) 62-70.
 
[5]  H. Saberi Najafi, S. A. Edalatpanah, On the Convergence Regions of Generalized AOR Methods for Linear Complementarity Problems. J. Optim. Theory. Appl., 156(2013) 859-866.
 
[6]  H. Saberi Najafi, S. A. Edalatpanah, On the Application of Liao's Method for Solving Linear Systems. Ain Shams Engineering Journal, 4 (2013) 501-505.
 
[7]  H. Saberi Najafi, S. A. Edalatpanah, A Note on “A new method for solving fully fuzzy linear programming problems”. Appl. Math. Model., 37 (2013) 7865-7867.
 
[8]  H. Saberi Najafi, S. A. Edalatpanah, On the Application of Liao's Method for Solving Linear Systems. Ain Shams Engineering Journal, 4 (2013) 501-505.
 
[9]  H. Saberi Najafi, S. A. Edalatpanah, A.H.Refahi Sheikhani, A new model of (I+S)-type preconditioner for system of linear equations. Journal of Mathematical Modeling, 1(2013) 1-14.
 
[10]  H. Saberi Najafi, S. A. Edalatpanah, G.A. Gravvanis, An Efficient Method for Computing the Inverse of Arrowhead Matrices. Applied Mathematics Letters, 33 (2014) 1-5.
 
[11]  H. Saberi Najafi, S. A. Edalatpanah, on the modified symmetric successive overrelaxation method for augmented systems. Computational and Applied Mathematics,(2014).
 
[12]  H. Saberi Najafi, S. A. Edalatpanah, A.H.Refahi Sheikhani, Convergence Analysis of Modified Iterative Methods to Solve Linear Systems. Mediterranean Journal of Mathematics, (2014).
 
[13]  J.H. He, Homotopy perturbation technique. Computational Methods in Applied Mechanics and Engineering, 178(1999), 257-262.
 
[14]  J.H. He, Application of HPM to nonlinear wave equations. Chaos, Solitons and Fractals. 26(2005) 695-700.
 
[15]  M. Dehghan, F. Shakeri, Use of He's homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, Journal of Porous Media.,11(2008)765-778.
 
[16]  J. Saberi-Nadjafi,A. Ghorbani, He’s homotopy perturbation method: An effective tool for solving nonlinear integral and integro-differential equations, Computers & Mathematics with Applications, 58(2009) 2379-2390.
 
[17]  F. Soltanian, M. Dehghan, S.M. Karbassi, Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications. International Journal of Computer Mathematics. 87(2010)1950-1974.
 
[18]  H. Saberi Najafi, S. A. Edalatpanah, Homotopy Perturbation Method for Linear Programming Problems. Appl. Math. Model. 38(2014), 1607-1611.
 
[19]  B. Karamati, An approach to the solution of linear system of equations by He’s homotopy perturbation method, Chaos. Solitons and Fractals., 41(2009)152-156.
 
[20]  H.K. Liu, Application of homotopy perturbation methods for solving systems of linear equations. Applied Mathematics and Computation., 61(2011) 2555-25561.
 
[21]  M.A. Noor, K.I. Noor, S. Khan, M. Waseem, Modified homotopy perturbation method for solving system of linear equations. Journal of the Association of Arab Universities for Basic and Applied Sciences. 13(2013)35-37.