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A modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations
Author(s) -
Ramadan Mohamed A.,
Bayoumi Ahmed M. E.
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1574
Subject(s) - conjugate gradient method , derivation of the conjugate gradient method , nonlinear conjugate gradient method , sylvester matrix , conjugate residual method , convergence (economics) , mathematics , gradient method , matrix (chemical analysis) , biconjugate gradient method , algorithm , iterative method , sylvester equation , mathematical optimization , gradient descent , computer science , mathematical analysis , artificial intelligence , eigenvalues and eigenvectors , artificial neural network , polynomial matrix , economic growth , materials science , physics , matrix polynomial , quantum mechanics , polynomial , economics , composite material
In this paper, we present a modified gradient‐based algorithm for solving extended Sylvester‐conjugate matrix equations. The idea is from the gradient‐based method introduced in [14] and the relaxed gradient‐based algorithm proposed in [16]. The convergence analysis of the algorithm is investigated. We show that the iterative solution converges to the exact solution for any initial value based on some appropriate assumptions. A numerical example is given to illustrate the effectiveness of the proposed method and to test its efficiency and accuracy compared with those presented in [14] and [16].
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