Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

Algorithms

Farahnaz Soleimani¹  Predrag S. Stanimirović²  Fazlollah Soleymani³  Alicia Cordero⁴  Juan R. Torregrosa⁴ 

[1] Department of Chemistry, Roudehen Branch, Islamic Azad University, 39731 Roudehen, Iran;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia; E-Mail:;Department of Applied Mathematics, Ferdowsi University of Mashhad, 91779 Mashhad, Iran; E-Mail:;id="af1-algorithms-08-00982">1Department of Chemistry, Roudehen Branch, Islamic Azad University, 39731 Roudehen, Ir

关键词: generalized inverses;    balancing chemical equations;    hyper-power method;    order of convergence;    matrix inverse;   

DOI  :  10.3390/a8040982

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.