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The iterative method for solving nonlinear matrix equation X s +A * X -t A=Q. (English) Zbl 1131.65039
The author provides necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the nonlinear matrix equation X s +A * X -t A=Q, where Q is an Hermitian positive definite matrix, A * is the conjugate transpose of the matrix A, and s,t are positive integers. In order to compute Hermitian positive definite solutions, an iterative method is derived. In addition, the author also provides a perturbation bound for the Hermitian positive definite solutions. Moreover some numerical examples are also presented.

MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities