Principal Subspace Flows Via Mechanical Systems on Grassmann Manifolds

DOI10.1007/978-3-540-73890-9_20zbMath1133.37024OpenAlexW123544142MaRDI QIDQ5436778

P. S. Krishnaprasad, Uwe R. Helmke

Publication date: 17 January 2008

Published in: Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-73890-9_20

zbMATH Keywords

dominant subspaceprincipal subspace analysissecond order mechanical system

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Applications of dynamical systems (37N99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Global Riemannian geometry, including pinching (53C20) Exterior algebra, Grassmann algebras (15A75)

Cites Work

• A simplified neuron model as a principal component analyzer
• A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics.
• Dissipation induced instabilities
• The Euler-Poincaré equations and double bracket dissipation
• Generic Observability of Differentiable Systems
• Hessian Riemannian Gradient Flows in Convex Programming
• Pointwise convergence of gradient‐like systems
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