Solvability for a Nonlinear Matrix Equation

Author:

Li J.,Zhang Y. H.

Publisher

Springer Science and Business Media LLC

Subject

Anesthesiology and Pain Medicine

Reference29 articles.

1. Anderson Jr., W.N., Morley, T.D., Trapp, G.E.: Positive solutions to $$X=A-BX^{-1}B^{H}$$ X = A - B X - 1 B H . Linear Algebra Appl. 134, 53–62 (1990)

2. Bhatia, R.: Matrix Analysis, Graduate Texts in Mathematics. Springer, Berlin (1997)

3. Duan, X.F., Li, C.M., Liao, A.P.: Solutions and perturbation analysis for the nonlinear matrix equation $$X+\sum \_{i=1}^{m}A\_{i}^{*}X^{-1}A\_{i}=I$$ X + ∑ _ i = 1 m A _ i ∗ X - 1 A _ i = I . Appl. Math. Comput. 218, 4458–4466 (2011)

4. Engwerda, J.C.: On the existence of a positive definite solution of the matrix equation $$X+A^TX^{-1}A=I$$ X + A T X - 1 A = I . Linear Algebra Appl. 194, 91–108 (1993)

5. Guo, C.H., Lancaster, P.: Iterative solution of two matrix equations. Math. Comp. 68, 1589–1603 (1999)

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1. On Hermitian positive definite solutions of a nonlinear matrix equation;Journal of Fixed Point Theory and Applications;2021-04-19

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