Computation of few Lyapunov exponents by geodesic based algorithms

Authors:
N. Del Buono;C. Elia
Affiliations:
Dipartimento Interuniversitario di Matematica, Università degli Studi di Bari, Via E. Orabona 4, I-70125 Bari, Italy;Dipartimento Interuniversitario di Matematica, Università degli Studi di Bari, Via E. Orabona 4, I-70125 Bari, Italy
Venue:
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Year:
2003

Citing 6
Cited 0

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Unitary integrators and applications to continuous orthonormalization techniques

SIAM Journal on Numerical Analysis
Computation of a few Lyapunov exponents for continuous and discrete dynamical systems

Applied Numerical Mathematics - Special issue on numerical methods for ordinary differential equations
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems

SIAM Journal on Numerical Analysis
The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we apply numerical methods based on the embedded geodesics for computing few Lyapunov exponents of a finite dimensional dynamical system. These new numerical algorithms are designed using geometric structure of the Stiefel manifold and they preserve orthogonality to machine accuracy. Numerical tests are also provided in order to show the features of our methods.