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Approximating the inverse and the Moore‐Penrose inverse of complex matrices
Author(s) -
Cordero Alicia,
Torregrosa Juan R.,
Zafar Fiza
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5879
Subject(s) - mathematics , inverse , convergence (economics) , moore–penrose pseudoinverse , matrix (chemical analysis) , parametric statistics , generalized inverse , order (exchange) , algebra over a field , pure mathematics , statistics , geometry , materials science , economics , composite material , economic growth , finance
A parametric family of fourth‐order schemes for computing the inverse and the Moore‐Penrose inverse of a complex matrix is designed. A particular value of the parameter allows us to obtain a fifth‐order method. Convergence analysis of the different methods is studied. Every iteration of the proposed schemes involves four matrix multiplications. A numerical comparison with other known methods, in terms of the average number of matrix multiplications and the mean of CPU time, is presented.