SVD algorithms to approximate spectra of dynamical systems

DOI10.1016/j.matcom.2008.03.005zbMath1166.65363OpenAlexW1999517614MaRDI QIDQ1010048

Cinzia Elia, Luca Dieci

Publication date: 3 April 2009

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2008.03.005

zbMATH Keywords

singular value decompositionLyapunov exponentsnumerical approximationexponential dicothomy

Mathematics Subject Classification ID

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) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items

Simple estimation method for the second-largest Lyapunov exponent of chaotic differential equations, The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects, Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems, Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems, Rotation number and exponential dichotomy for linear Hamiltonian systems: from theoretical to numerical results, Detecting exponential dichotomy on the real line: SVD and QR algorithms, Exponential dichotomy on the real line: SVD and QR methods, Time-varying rational expectations models

Uses Software

• psSchur

Cites Work

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• The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects
• The calculation of Lyapunov spectra
• Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• Differential equations for the analytic singular value decomposition of a matrix
• A spectral theory for linear differential systems
• Dichotomies in stability theory
• Local Lyapunov exponents computed from observed data
• Normally hyperbolic invariant manifolds in dynamical systems
• Orthosymplectic integration of linear Hamiltonian systems
• 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.
• A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles.
• On graded QR decompositions of products of matrices
• 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
• Solving Ordinary Differential Equations I
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Computing the Singular Value Decomposition of a Product of Two Matrices
• Computing Lyapunov spectra with continuous Gram - Schmidt orthonormalization
• Hill's equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena
• On Smooth Decompositions of Matrices
• Chaos in Dynamical Systems
• Lyapunov Spectral Intervals: Theory and Computation
• A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN
• IMPROVED NUMERICAL FLOQUET MULTIPLIERS