04432nam a22006015i 4500 978-3-031-71326-2 DE-He213 20251030114617.0 cr nn 008mamaa 241214s2024 sz | s |||| 0|eng d 9783031713262 978-3-031-71326-2 10.1007/978-3-031-71326-2 doi QA370-380 PBKJ bicssc MAT007000 bisacsh PBKJ thema Gillis, Nicolas. author. aut http://id.loc.gov/vocabulary/relators/aut 88897 Recent Stability Issues for Linear Dynamical Systems [electronic resource] : Cetraro, Italy 2021 / by Nicolas Gillis, Nicola Guglielmi, Christian Lubich, Volker Mehrmann, Punit Sharma, Bart Vandereycken ; edited by Nicola Guglielmi, Christian Lubich. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 176 p. 18 illus., 15 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda C.I.M.E. Foundation Subseries, 2946-1820 ; 2357 Introduction -- Chapter 1. Solving Matrix Nearness Problems via Hamiltonian Systems, Matrix Factorization and Optimisation -- Chapter 2. Eigenvalue Optimization and Matrix Nearness Problems via Constrained Gradient Systems -- Chapter 3. Regularity, Stability, Passivity and Controllability of Structured Linear Descriptor Systems -- Chapter 4. Algorithms for Eigenvalue Optimization Related to Stability of Dynamical Systems. This book concerns matrix nearness problems in the framework of spectral optimization. It addresses some current research directions in spectral-based stability studies for differential equations, with material on ordinary differential equations (ODEs), differential algebraic equations and dynamical systems. Here, ‘stability’ is interpreted in a broad sense which covers the need to develop stable and reliable algorithms preserving some qualitative properties of the computed solutions, methodologies which are helpful to assess the onset of potential instabilities or loss of robustness, and tools to determine the asymptotic properties of the solution or its discretization. The topics considered include the computation of robustness measures for linear problems, the use of low-rank ODEs to approximate such measures via gradient systems, the regularity, stability, passivity and controllability analysis of structured linear descriptor systems, and the use of acceleration techniques to deal with some of the presented computational problems. Although the emphasis is on the numerical study of differential equations and dynamical systems, the book will also be of interest to researchers in matrix theory, spectral optimization and spectral graph theory, as well as in dynamical systems and systems theory. Differential equations. Dynamical systems. Differential Equations. Dynamical Systems. Guglielmi, Nicola. author. aut http://id.loc.gov/vocabulary/relators/aut 88898 Lubich, Christian. author. aut http://id.loc.gov/vocabulary/relators/aut 88899 Mehrmann, Volker. author. aut http://id.loc.gov/vocabulary/relators/aut 88900 Sharma, Punit. author. aut http://id.loc.gov/vocabulary/relators/aut 88901 Vandereycken, Bart. author. aut http://id.loc.gov/vocabulary/relators/aut 88902 Guglielmi, Nicola. editor. edt http://id.loc.gov/vocabulary/relators/edt 88898 Lubich, Christian. editor. edt http://id.loc.gov/vocabulary/relators/edt 88899 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031713255 Printed edition: 9783031713279 C.I.M.E. Foundation Subseries, 2946-1820 ; 2357 85459 https://doi.org/10.1007/978-3-031-71326-2 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 65696 65696