TY - GEN A1 - Vu Hoang, Linh A1 - Mehrmann, Volker T1 - Spectral Intervals for Differential-Algebraic Equations and their Numerical Approximation N2 - Lyapunov and exponential dichotomy spectral theory is extended from ordinary differential equations (ODEs) to nonautonomous differential-algebraic equations (DAEs). By using orthogonal changes of variables, the original DAE system is transformed into appropriate condensed forms, for which concepts such as Lyapunov exponents, Bohl exponents, exponential dichotomy and spectral intervals of various kinds can be analyzed via the resulting underlying ODE. Some essential differences between the spectral theory for ODEs and that for DAEs are pointed out. Numerical methods for computing the spectral intervals associated with Lyapunov and Sacker-Sell (exponential dichotomy) spectra are derived by modifying and extending those methods proposed for ODEs. Perturbation theory and error analysis are discussed, as well. Finally, some numerical examples are presented to illustrate the theoretical results and the properties of the numerical methods. KW - differential-algebraic equations KW - strangeness KW - index KW - Lyapunov exponent KW - Bohl exponent KW - Sacker-Sell spectrum KW - exponential dichotomy KW - spectral interval KW - smooth QR factorization KW - continuous QR algorithm KW - discrete QR algorithm KW - kinematic KW - equivalence KW - Steklov function Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/414 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4144 ER -