Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits.
Jason D. Mireles-JamesPublished in: Commun. Nonlinear Sci. Numer. Simul. (2015)
Keyphrases
- computer assisted
- error bounds
- higher dimensional
- linear approximation
- arbitrary dimension
- euclidean space
- low dimensional
- high dimensional
- theoretical analysis
- computer aided
- worst case
- manifold learning
- lower dimensional
- dynamical systems
- basis functions
- riemannian manifolds
- metric space
- distance transform
- policy iteration
- locality preserving projections
- data points
- vector space
- markov decision processes
- shape analysis
- feature space
- geodesic distance
- optimal solution
- reproducing kernel hilbert space
- high dimensional data
- locally linear embedding
- dimensionality reduction
- dynamic programming
- machine learning