Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations
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 impr...
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doaj-714678a5fc944cf8bd47582d456b99b72020-11-25T00:08:12ZengMDPI AGAlgorithms1999-48932015-11-018498299810.3390/a8040982a8040982Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical EquationsFarahnaz Soleimani0Predrag S. Stanimirovi´c1Fazlollah Soleymani2Department of Chemistry, Roudehen Branch, Islamic Azad University, 39731 Roudehen, IranFaculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, SerbiaDepartment of Applied Mathematics, Ferdowsi University of Mashhad, 91779 Mashhad, IranAn 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.http://www.mdpi.com/1999-4893/8/4/982generalized inversesbalancing chemical equationshyper-power methodorder of convergencematrix inverse |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Farahnaz Soleimani Predrag S. Stanimirovi´c Fazlollah Soleymani |
spellingShingle |
Farahnaz Soleimani Predrag S. Stanimirovi´c Fazlollah Soleymani Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations Algorithms generalized inverses balancing chemical equations hyper-power method order of convergence matrix inverse |
author_facet |
Farahnaz Soleimani Predrag S. Stanimirovi´c Fazlollah Soleymani |
author_sort |
Farahnaz Soleimani |
title |
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations |
title_short |
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations |
title_full |
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations |
title_fullStr |
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations |
title_full_unstemmed |
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations |
title_sort |
some matrix iterations for computing generalized inverses and balancing chemical equations |
publisher |
MDPI AG |
series |
Algorithms |
issn |
1999-4893 |
publishDate |
2015-11-01 |
description |
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. |
topic |
generalized inverses balancing chemical equations hyper-power method order of convergence matrix inverse |
url |
http://www.mdpi.com/1999-4893/8/4/982 |
work_keys_str_mv |
AT farahnazsoleimani somematrixiterationsforcomputinggeneralizedinversesandbalancingchemicalequations AT predragsstanimirovic somematrixiterationsforcomputinggeneralizedinversesandbalancingchemicalequations AT fazlollahsoleymani somematrixiterationsforcomputinggeneralizedinversesandbalancingchemicalequations |
_version_ |
1725416209160077312 |