Titlebook: Algorithms for Quadratic Matrix and Vector Equations; Federico Poloni Book 2011 The Editor(s) (if applicable) and The Author(s), under exc

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Nonsymmetric algebraic Riccati equationsithms for their solution has had a strong acceleration in the last decade. Important progresses have been obtained concerning theoretical properties of this class of matrix equations and new effective algorithms relying on the properties of M-matrices have been designed and analyzed [15, 39, 33, 32,

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Newton method for rank-structured algebraic Riccati equations[100]. The solution of interest is the minimal positive one, whose existence is proved in [100]. Note that for this equation . is an M-matrix [70]: in fact, . by Lemma 1.2.2 this is an M-matrix if and only if . which reduces to . in view of (11). According to the terminology in (5.2.2), the equation

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