Solving Large Sparse Lyapunov Equations on Parallel Computers (Research Note)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Sylvester equations and projection-based model reduction
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Proceedings of the 43rd annual Design Automation Conference
Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations
Applied Numerical Mathematics
Trail to a Lyapunov equation solver
Computers & Mathematics with Applications
Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems
Large-Scale Scientific Computing
On the ADI method for Sylvester equations
Journal of Computational and Applied Mathematics
Approximation of low rank solutions for linear quadratic control of partial differential equations
Computational Optimization and Applications
Parallel solution of band linear systems in model reduction
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
An invariant subspace method for large-scale algebraic Riccati equation
Applied Numerical Mathematics
On the numerical solution of large-scale sparse discrete-time Riccati equations
Advances in Computational Mathematics
Krylov subspace methods for projected Lyapunov equations
Applied Numerical Mathematics
A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations
SIAM Journal on Matrix Analysis and Applications
Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
SIAM Journal on Control and Optimization
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
Parallel solution of large-scale and sparse generalized algebraic riccati equations
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Parallel order reduction via balanced truncation for optimal cooling of steel profiles
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Parallel algorithms for balanced truncation model reduction of sparse systems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
An efficient algorithm for solving general coupled matrix equations and its application
Mathematical and Computer Modelling: An International Journal
An improved algorithm for balanced POD through an analytic treatment of impulse response tails
Journal of Computational Physics
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
Automatica (Journal of IFAC)
On the ADI method for the Sylvester equation and the optimal-H2 points
Applied Numerical Mathematics
Accelerating the Lyapack library using GPUs
The Journal of Supercomputing
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Hi-index | 0.01 |
In this paper we present the cyclic low-rank Smith method, which is an iterative method for the computation of low-rank approximations to the solution of large, sparse, stable Lyapunov equations. It is based on a generalization of the classical Smith method and profits by the usual low-rank property of the right-hand side matrix. The requirements of the method are moderate with respect to both computational cost and memory. Furthermore, we propose a heuristic for determining a set of suboptimal alternating direction implicit (ADI) shift parameters. This heuristic, which is based on a pair of Arnoldi processes, does not require any a priori knowledge on the spectrum of the coefficient matrix of the Lyapunov equation. Numerical experiments show the efficiency of the iterative scheme combined with the heuristic for the ADI parameters.