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A new iterative method for solving large-scale Lyapunov matrix equations. (English) Zbl 1146.65038

A new projection method to solve large-scale continuous-time Lyapunov matrix equations of the type \[ AX + XA^T + BB^T = 0, \] where \(A \in \mathbb R^{n \times n}\) and \(B \in \mathbb R^{n \times s}\), with \(s \leq n\), is proposed. The method projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in \(A\) and \(A^{-1}\). The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the competitiveness of the new method, compared to a state-of-the-art approach based on the factorized alternating direction implicit iteration.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities

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