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Algorithms 2015, 8(4), 982-998; doi:10.3390/a8040982

Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

1
Department of Chemistry, Roudehen Branch, Islamic Azad University, 39731 Roudehen, Iran
2
Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
3
Department of Applied Mathematics, Ferdowsi University of Mashhad, 91779 Mashhad, Iran
*
Author to whom correspondence should be addressed.
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 25 June 2015 / Revised: 24 October 2015 / Accepted: 26 October 2015 / Published: 3 November 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [407 KB, uploaded 3 November 2015]   |  

Abstract

An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished. View Full-Text
Keywords: generalized inverses; balancing chemical equations; hyper-power method; order of convergence; matrix inverse generalized inverses; balancing chemical equations; hyper-power method; order of convergence; matrix inverse
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Soleimani, F.; Stanimirovi´c, P.S.; Soleymani, F. Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations. Algorithms 2015, 8, 982-998.

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