Finite-Rank ADI Iteration for Operator Lyapunov Equations

DOI10.1137/120885310zbMath1279.93022OpenAlexW2066059560MaRDI QIDQ2873868

Timo Reis, Mark R. Opmeer, Winnifried Wollner

Publication date: 27 January 2014

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: http://opus.bath.ac.uk/37724/1/88531.pdf

zbMATH Keywords

heat equationLyapunov equationalternating direction implicit (ADI) iterationnumerical method in control theoryinfinite-dimensional linear systems theory

Mathematics Subject Classification ID

Related Items (14)

Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces ⋮ Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces ⋮ Decay of singular values for infinite-dimensional systems with Gevrey regularity ⋮ On the Approximability of Koopman-Based Operator Lyapunov Equations ⋮ Stabilization of nonautonomous linear parabolic-like equations: oblique projections versus Riccati feedbacks ⋮ Inexact methods for the low rank solution to large scale Lyapunov equations ⋮ On the eigenvalue decay of solutions to operator Lyapunov equations ⋮ Balancing transformations for infinite-dimensional systems with nuclear Hankel operator ⋮ Sparsity preserving optimal control of discretized PDE systems ⋮ Balanced Truncation Based on Generalized Multiscale Finite Element Method for the Parameter-Dependent Elliptic Problem ⋮ The ADI method for bounded real and positive real Lur'e equations ⋮ Optimality of balanced proper orthogonal decomposition for data reconstruction. II: Further approximation results ⋮ Analysis of an Iteration Method for the Algebraic Riccati Equation ⋮ Sparse Grid Approximation of the Riccati Operator for Closed Loop Parabolic Control Problems with Dirichlet Boundary Control

Uses Software

• deal.ii

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