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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Jürgen Isberg,Hans-Horst RosackerThe problem of reducing an algebraic Riccati equation (5) to a unilateral quadratic matrix equation (2) has been considered in [32, 73, 95, 109, 138].

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Storage-optimal algorithms for Cauchy-like matricesSeveral classes of algorithms for the numerical solution of Toeplitz-like and Cauchy-like linear systems exist in the literature. We refer the reader to [153] for an extended introduction on this topic, with descriptions of each method and plenty of citations to the relevant papers, and only summarize them in Table 7.1.

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https://doi.org/10.33283/978-3-86298-846-4se 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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Jürgen Isberg,Hans-Horst Rosackererical algorithms, taken mainly from [31]. Moreover, we describe several attempts to generalize the logarithmic reduction algorithm to a generic quadratic vector equation in the framework of Chapter 2, that lead to an unexpected connection with Newton’s algorithm. While the original results containe