The calculation of Lyapunov spectra
Physica D
A New Software Package for Linear Differential-Algebraic Equations
SIAM Journal on Scientific Computing
On Smooth Decompositions of Matrices
SIAM Journal on Matrix Analysis and Applications
Lyapunov Spectral Intervals: Theory and Computation
SIAM Journal on Numerical Analysis
On the Error in QR Integration
SIAM Journal on Numerical Analysis
SVD algorithms to approximate spectra of dynamical systems
Mathematics and Computers in Simulation
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
A hybrid method for computing Lyapunov exponents
Numerische Mathematik
Adjoint pairs of differential-algebraic equations and Hamiltonian systems
Applied Numerical Mathematics
Advances in Computational Mathematics
Journal of Computational and Applied Mathematics
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This paper is devoted to the numerical approximation of Lyapunov and Sacker-Sell spectral intervals for linear differential-algebraic equations (DAEs). The spectral analysis for DAEs is improved and the concepts of leading directions and solution subspaces associated with spectral intervals are extended to DAEs. Numerical methods based on smooth singular value decompositions are introduced for computing all or only some spectral intervals and their associated leading directions. The numerical algorithms as well as implementation issues are discussed in detail and numerical examples are presented to illustrate the theoretical results.