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Iterative solution of two matrix equations. (English) Zbl 0940.65036
Iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X+A * X -1 A=Q and X-A * A -1 A=Q are studied. Here Q is Hermitian positive definite and the ordering XY if X-Y is positive semidefinite. The convergence rates of various algorithms depend on the eigenvalues of (X + ) -1 A, where X + is a solution. These eigenvalues are related to the eigenvalues of a matrix pencil which is independent of X + .

MSC:
65F10Iterative methods for linear systems
65F30Other matrix algorithms
15A22Matrix pencils
15A24Matrix equations and identities