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Perturbation estimates for the nonlinear matrix equation $X-A^*X^qA=Q$ ($0<q<1$). (English) Zbl 1214.15007
The nonlinear matrix equation $X - A^{*} X^{q} A=Q$ with $0<q<1$ is investigated. Two perturbation estimates for the unique positive definite solution of the equation are derived. The theoretical results are illustrated by numerical examples.

15A24Matrix equations and identities
65F30Other matrix algorithms
Full Text: DOI
[1] Ferrante, A., Levy, B.C.: Hermitian solution of the equation X=Q+NX N *. Linear Algebra Appl. 247, 359--373 (1996) · Zbl 0876.15011 · doi:10.1016/0024-3795(95)00121-2
[2] Zhang, Y.H.: On Hermitian positive definite solutions of matrix equation X+A * X A=I. Linear Algebra Appl. 372, 295--304 (2003) · Zbl 1035.15017 · doi:10.1016/S0024-3795(03)00530-5
[3] Hasanov, V., Ivanov, I.: Solutions and perturbation estimates for of the matrix equation X{$\pm$}A * X A=Q. Appl. Math. Comput. 156, 513--525 (2004) · Zbl 1063.15012 · doi:10.1016/j.amc.2003.08.007
[4] Zhang, Y.H., Wang, J.F., Zhu, B.R.: The Hermitian positive definite solutions of matrix equation X+A * X A=I. J. Numer. Math. Appl. 26, 14--27 (2004)
[5] Gao, D.J., Zhang, Y.H.: Hermitian positive definite solutions of matrix equation X * X q A=Q (q>0). J. Numer. Math. Appl. 29, 73--80 (2007) · Zbl 1121.15302
[6] Gao, D.J., Zhang, Y.H.: Perturbation analysis of the Hermitian positive definite solutions of matrix equation X * X q A=I (0<q<1). J. Numer. Math. Appl. 29, 403--412 (2007) · Zbl 1141.15320