Inversion free Iterative Method for Finding Symmetric Solution of the Nonlinear Matrix Equation 𝑿 − 𝑨∗𝑿𝒒𝑨 = 𝑰 (𝒒 ≥ 𝟐)
Keyword(s):
In this paper, we propose the inversion free iterative method to find symmetric solution of thenonlinear matrix equation 𝑿 − 𝑨∗𝑿𝒒𝑨 = 𝑰 (𝒒 ≥ 𝟐), where 𝑋 is an unknown symmetricsolution, 𝐴 is a given Hermitian matrix and 𝑞 is a positive integer. The convergence of theproposed method is derived. Numerical examples demonstrate that the proposed iterative methodis quite efficient and converges well when the initial guess is sufficiently close to the approximatesolution. Keywords: Symmetric solution, nonlinear matrix equation, inversion free, iterative method
2020 ◽
Vol 153
◽
pp. 503-518
◽
Keyword(s):
2021 ◽
Vol 1903
(1)
◽
pp. 012024
2007 ◽
Vol 188
(1)
◽
pp. 46-53
◽
2011 ◽
Vol 2011
◽
pp. 1-18
◽
2001 ◽
Vol 23
(1)
◽
pp. 295-302
◽
Keyword(s):