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Improved perturbation estimates for the matrix equations X±A * X -1 A=Q. (English) Zbl 1039.15005
The authors give new and improved perturbation estimates for the solutions of the matrix quadratic equations X±A * X -1 A=Q (X and Q are positive definite Hermitian matrices). Some of the estimates depend and some do not depend on the knowledge of the exact solution X. The results are compared with those of S. F. Xu [Linear Algebra Appl. 336, 61–70 (2001; Zbl 0992.15013)] and of A. C. M. Ran and M. C. B. Reurings [Linear Algebra Appl. 346, 15–26 (2002; Zbl 1086.15013)]. The paper contains a presentation of numerical experiments.

MSC:
15A24Matrix equations and identities
15A45Miscellaneous inequalities involving matrices
65F35Matrix norms, conditioning, scaling (numerical linear algebra)