Open AccessOn the solutions to Sylvester‐conjugate periodic matrix equations via iteration
Author(s) -
Zhang Lei,
Li Pengxiang,
Han Mengqi,
Zhang Yanfeng,
Chang Rui,
Zhang Jinhua
Publication year - 2023
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/cth2.12312
Subject(s) - conjugate gradient method , sylvester matrix , sylvester equation , mathematics , matrix (chemical analysis) , derivation of the conjugate gradient method , iterative method , conjugate residual method , convergent matrix , eight point algorithm , sequence (biology) , state transition matrix , class (philosophy) , mathematical optimization , gradient descent , computer science , symmetric matrix , mathematical analysis , artificial intelligence , polynomial matrix , artificial neural network , eigenvalues and eigenvectors , composite material , genetics , biology , quantum mechanics , physics , matrix polynomial , materials science , polynomial
Abstract The problem of solving a class of Sylvester‐conjugate periodic matrix equations is investigated in this paper. Utilising conjugate gradient method, an iterative algorithm is provided, from which a matrix sequence can be generated to approximate the unknown matrix of the equation to be solved. Theoretical derivation proves that the proposed algorithm is convergent starting from any initial value, and simulation examples show the effectiveness of the proposed algorithm.