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The symmetric linear matrix equation. (English) Zbl 1002.15015

The authors study solutions to the equations

X±(A 1 * XA 1 +...+A m * XA m )=Q

which occur in the Newton method applied to algebraic Riccati equations. Conditions are found for these equations to have unique solutions, and an explicit formula is given in the case when there is a unique positive definite solution.

MSC:
15A24Matrix equations and identities