Algorithms for Quadratic Matrix and Vector Equations

1. Linear algebra preliminaries
Federico Poloni

Part I. Quadratic vector and matrix equations

2. Quadratic vector equations
Federico Poloni

3. A Perron vector iteration for QVEs
Federico Poloni

4. Unilateral quadratic matrix equations
Federico Poloni

5. Nonsymmetric algebraic Riccati equations
Federico Poloni

6. Transforming NAREs into UQMEs
Federico Poloni

Part II. Rank-structured NAREs

7. Storage-optimal algorithms for Cauchy-like matrices
Federico Poloni

8. Newton method for rank-structured algebraic Riccati equations
Federico Poloni

Part III. Matrix equations from control theory

9. Lur’e equations
Federico Poloni

10. Generalized SDA
Federico Poloni

Part IV. Matrix geometric means

11. An effective matrix geometric mean
Federico Poloni

12. Constructing other matrix geometric means
Federico Poloni

13. Conclusions
Federico Poloni

Keywords: Mathematics, Algebra