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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Book 2011 forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results

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An effective matrix geometric mean on this manifold the geodesic joining . and . has equation . and thus . is the midpoint of the geodesic joining . and . An analysis of numerical methods for computing the geometric mean of two matrices is carried out in [96].

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,C. Mündliche Verhandlung vom 10. und, on this manifold the geodesic joining . and . has equation . and thus . is the midpoint of the geodesic joining . and . An analysis of numerical methods for computing the geometric mean of two matrices is carried out in [96].

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Linear algebra preliminariesse of . The notation I., with . often omitted when it is clear from the context, denotes the identity matrix; the zero matrix of any dimension is denoted simply by 0. With . we denote the vector of suitable dimension all of whose entries are 1. The expression ρ (.) stands for the spectral radius of

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Quadratic vector equationsthese problems have been studied extensively in the past by several authors. For references to the single equations and results, we refer the reader to the following sections, in particular Section 2.3. Many of the results appearing here have already been proved for one or more of the single instanc

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