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Computing the extremal positive definite solutions of a matrix equation. (English) Zbl 0856.65044
An implementation of a well-known algorithm is proposed for finding extremal positive definite solutions of the matrix equation X+A * X -1 A=I. The convergence rate is analyzed. Then a new algorithm is presented. This algorithm avoids matrix inversions.
MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities