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On Hermitian positive definite solutions of matrix equation X-A * X -2 A=I * . (English) Zbl 1087.15020
The author studies the Hermitian positive definite solutions of the matrix equation X-A * X -2 A=I, where I is the n×n identity matrix and A is an n×n complex matrix. A theorem on the existence of solutions is given for every complex matrix A, and the solution is given in case that A is normal or unitary. An estimation of the solution is proposed by using a fixed point iteration method and a discussion for the convergence behavior of this method is given. The whole theory is illustrated by several numerical examples.
MSC:
15A24Matrix equations and identities
65F30Other matrix algorithms