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Perturbation analysis of the Hermitian positive definite solutions of the matrix equation X-A * X q A=I(0<q<1). (Chinese) Zbl 1141.15320
Summary: The paper considers the nonlinear matrix equation X-A * X q A=I with 0<q<1. it shows that there exists a unique positive definite solution to the equation. A perturbation bound for the unique solution to the equation is derived, and it shows that the equation is well-posed. Explicit expressions of the condition number for the unique positive definite solution are obtained, and the backward error of an approximate solution to the unique positive definite solution is evaluated. The results are illustrated by numerical examples.
MSC:
15A24Matrix equations and identities
65F30Other matrix algorithms