Two kinds of algorithms are usually resorted to in order to solve the well-known Lyapounov discrete equationATXA - X = Q: transformation of the original linear system in a classical one withn(n + 1)/2unknowns, and iterative scheme [1]. The first requiresn⁴/4storage words and a cost ofn⁶/3multiplications, which is impractical with a large system, and the second applies only ifAis a stable matrix. The solution proposed requires no stability assumption and operates in only some n2words and n3multiplications.
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A. Barraud (1977) studied this question.
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