Open AccessMatrix GPBiCG algorithms for solving the general coupled matrix equations
Author(s) -
Hajarian Masoud
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0669
Subject(s) - kronecker product , matrix (chemical analysis) , sylvester equation , sylvester matrix , mathematics , matrix splitting , convergent matrix , symmetric matrix , matrix exponential , state transition matrix , algorithm , matrix function , conjugate gradient method , kronecker delta , differential equation , mathematical analysis , polynomial matrix , eigenvalues and eigenvectors , materials science , physics , matrix polynomial , quantum mechanics , polynomial , composite material
Linear matrix equations have important applications in control and system theory. In the study, we apply Kronecker product and vectorisation operator to extend the generalised product bi‐conjugate gradient (GPBiCG) algorithms for solving the general coupled matrix equations ∑ lj =1 ( A ) i , 1 , j X 1 B i , 1, j + A i , 2, j X 2 B i, 2, j +…+ A i,l,j X i,l,j ) = D i for i = 1,2,…, l (including the (coupled) Sylvester, the second‐order Sylvester and coupled Markovian jump Lyapunov matrix equations). We propose four effective matrix algorithms for finding solutions of the matrix equations. Numerical examples and comparison with other well‐known algorithms demonstrate the effectiveness of the proposed matrix algorithms.