The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects
From MaRDI portal
Publication:860745
DOI10.1016/j.jde.2006.08.007zbMath1139.93014OpenAlexW1963815527MaRDI QIDQ860745
Publication date: 9 January 2007
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2006.08.007
Lyapunov and storage functions (93D30) Eigenvalue problems (93B60) Eigenvalues, singular values, and eigenvectors (15A18) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Numerical investigation of stability of solutions to ordinary differential equations (65L07)
Related Items (12)
Angular Values of Nonautonomous Linear Dynamical Systems: Part II – Reduction Theory and Algorithm ⋮ Projected Shadowing-Based Data Assimilation ⋮ Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study ⋮ Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps ⋮ Rotation number and exponential dichotomy for linear Hamiltonian systems: from theoretical to numerical results ⋮ Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations ⋮ Detecting exponential dichotomy on the real line: SVD and QR algorithms ⋮ On new estimates for Lyapunov exponents of discrete time varying linear systems ⋮ SVD algorithms to approximate spectra of dynamical systems ⋮ Exponential dichotomy on the real line: SVD and QR methods ⋮ NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION ⋮ Angular Values of Nonautonomous and Random Linear Dynamical Systems: Part I---Fundamentals
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- SVD algorithms to approximate spectra of dynamical systems
- The calculation of Lyapunov spectra
- Numerical computation of an analytic singular value decomposition of a matrix valued function
- Differential equations for the analytic singular value decomposition of a matrix
- A spectral theory for linear differential systems
- Dichotomies in stability theory
- The structurally stable linear systems on the half-line are those with exponential dichotomies
- A new algorithm for the SVD of a long product of matrices and the stability of products
- Smooth SVD on the Lorentz group with application to computation of Lyapunov exponents.
- Exponential splittings of products of matrices and accurately computing singular values of long products
- Lyapunov and Sacker-Sell spectral intervals
- Comparison of Different Methods for Computing Lyapunov Exponents
- On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
- Ergodic Properties of Linear Dynamical Systems
- On Smooth Decompositions of Matrices
- Ergodic theory of chaos and strange attractors
- Lyapunov Spectral Intervals: Theory and Computation
- Normal Forms and Unfoldings for Local Dynamical Systems
This page was built for publication: The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects