Kernel Methods for Discrete-Time Linear Equations

Methods from learning theory are used in the state space of linear dynamical systems in order to estimate the system matrices and some relevant quantities such as a the topological entropy.

[1]  S. Smale,et al.  Shannon sampling and function reconstruction from point values , 2004 .

[2]  G. Wahba Spline models for observational data , 1990 .

[3]  Felipe Cucker,et al.  On the mathematical foundations of learning , 2001 .

[4]  W. Kliemann,et al.  Dynamical Systems and Linear Algebra , 2014 .

[5]  Lennart Ljung,et al.  Kernel methods in system identification, machine learning and function estimation: A survey , 2014, Autom..

[6]  M. Fréchet Sur La Definition Axiomatique D'Une Classe D'Espaces Vectoriels Distancies Applicables Vectoriellement Sur L'Espace de Hilbert , 1935 .

[7]  R. Rifkin,et al.  Notes on Regularized Least Squares , 2007 .

[8]  N. Aronszajn Theory of Reproducing Kernels. , 1950 .

[9]  I. J. Schoenberg On Certain Metric Spaces Arising From Euclidean Spaces by a Change of Metric and Their Imbedding in Hilbert Space , 1937 .

[10]  P. Walters Introduction to Ergodic Theory , 1977 .

[11]  Ding-Xuan Zhou,et al.  Learning Theory Approach to a System Identification Problem Involving Atomic Norm , 2015 .

[12]  S. Smale,et al.  ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY , 2003 .

[13]  Ding-Xuan Zhou,et al.  Capacity of reproducing kernel spaces in learning theory , 2003, IEEE Transactions on Information Theory.

[14]  Tomaso A. Poggio,et al.  Regularization Networks and Support Vector Machines , 2000, Adv. Comput. Math..

[15]  JAKE BOUVRIE,et al.  Kernel Methods for the Approximation of Nonlinear Systems , 2011, SIAM J. Control. Optim..

[16]  Ward Cheney,et al.  A course in approximation theory , 1999 .

[17]  I. J. Schoenberg Remarks to Maurice Frechet's Article ``Sur La Definition Axiomatique D'Une Classe D'Espace Distances Vectoriellement Applicable Sur L'Espace De Hilbert , 1935 .

[18]  I. J. Schoenberg,et al.  Metric spaces and positive definite functions , 1938 .

[19]  S. Smale,et al.  Shannon sampling II: Connections to learning theory , 2005 .