Computing the extremal positive definite solutions of a matrix equation. (English) Zbl 0856.65044

Zhan, Xingzhi

SIAM J. Sci. Comput. 17, No. 5, 1167-1174 (1996).

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.

Reviewer: P.Y.Yalamov (Russe)

MSC:

65F30	Other matrix algorithms (MSC2010)
65F10	Iterative numerical methods for linear systems
15A24	Matrix equations and identities

Keywords:

iteration; algorithm; extremal positive definite solutions; matrix equation; convergence