Numerical low-rank approximation of matrix differential equations

[1]  Peter Benner,et al.  Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations , 2018, J. Num. Math..

[2]  Hermann Mena,et al.  Numerical solution of the finite horizon stochastic linear quadratic control problem , 2017, Numer. Linear Algebra Appl..

[3]  Hanna Walach,et al.  Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values , 2016, SIAM J. Numer. Anal..

[4]  Alexander Ostermann,et al.  Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions , 2015, SIAM J. Sci. Comput..

[5]  Marco Caliari,et al.  The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential , 2015, SIAM J. Sci. Comput..

[6]  Tony Stillfjord,et al.  Low-Rank Second-Order Splitting of Large-Scale Differential Riccati Equations , 2015, IEEE Transactions on Automatic Control.

[7]  Alexander Ostermann,et al.  Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions , 2014, SIAM J. Sci. Comput..

[8]  S. Güttel Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection , 2013 .

[9]  Peter Benner,et al.  Rosenbrock Methods for Solving Riccati Differential Equations , 2013, IEEE Transactions on Automatic Control.

[10]  C. Lubich,et al.  A projector-splitting integrator for dynamical low-rank approximation , 2013, BIT Numerical Mathematics.

[11]  I. Petersen,et al.  Robust Control Design Using H-? Methods , 2012 .

[12]  Awad H. Al-Mohy,et al.  Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators , 2011, SIAM J. Sci. Comput..

[13]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[14]  Christian Lubich,et al.  Dynamical low-rank approximation: applications and numerical experiments , 2008, Math. Comput. Simul..

[15]  Valeria Simoncini,et al.  A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations , 2007, SIAM J. Sci. Comput..

[16]  Othmar Koch,et al.  Dynamical Low-Rank Approximation , 2007, SIAM J. Matrix Anal. Appl..

[17]  John Sabino,et al.  Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Methods , 2006 .

[18]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[19]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[20]  H. Abou-Kandil,et al.  Matrix Riccati Equations in Control and Systems Theory , 2003, IEEE Transactions on Automatic Control.

[21]  Y. Zhou,et al.  On the decay rate of Hankel singular values and related issues , 2002, Syst. Control. Lett..

[22]  Tyrone E. Duncan,et al.  Stochastic controls: Hamiltonian systems and HJB equations [Book Reviews] , 2001, IEEE Transactions on Automatic Control.

[23]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[24]  Prashant D. Sardeshmukh,et al.  The Optimal Growth of Tropical Sea Surface Temperature Anomalies , 1995 .

[25]  L. Dieci,et al.  Positive definiteness in the numerical solution of Riccati differential equations , 1994 .

[26]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[27]  Luca Dieci,et al.  Numerical integration of the differential Riccati equation and some related issues , 1992 .

[28]  Y. Saad Analysis of some Krylov subspace approximations to the matrix exponential operator , 1992 .

[29]  A. J. Laub,et al.  Efficient matrix-valued algorithms for solving stiff Riccati differential equations , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[30]  N. Higham COMPUTING A NEAREST SYMMETRIC POSITIVE SEMIDEFINITE MATRIX , 1988 .

[31]  J. Case A Simple Predictive Model for El Niño , 2009 .