Low rank solution of Lyapunov equations. SIAM Journal on Matrix Analysis and Applications 2002; 24(1):260-280.Li, J.R., White, J.: Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl. 24(1), 260-280 (2002)Li J R and White J. Low-rank solution of Lyapunov ...
The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky ...
Large-scaleMatrixdifferentialequationsLow-rankRiccatiequationsLyapunovequationsWe propose efficient algorithms for solving large-SaakTech Saak,Jens,Mena,... - 《Linear Algebra & Its Applications》 被引量: 41发表: 2015年 Low rank solution of data-sparse Sylvester equations In this paper, a method for...
Low rank methods for a class of generalized Lyapunov equations and related issues. Numer Math. 2013;124(3):441–70. https://doi.org/10.1007/s00211-013-0521-0. Article MathSciNet MATH Google Scholar Benner P, Li R-C, Truhar N. On the ADI method for Sylvester equations. J Comput ...
generalized Lyapunov equationGalerkin projectionThis work is concerned with the numerical solution of large‐scale linear matrix equations A1XB1T++AKXBKT=C . The most straightforward approach computes X∈Rm×n from the solution of an mn × mn linear system, typically limiting the feasible values of...
Inexact methods for the low rank solution to large scale Lyapunov equations Article 18 June 2020 Use our pre-submission checklist Avoid common mistakes on your manuscript. 1 Introduction We are interested in the numerical solution of general linear matrix equations of the form ∑i=1pAiXBiT+...
We investigate the numerical solution to a low rank perturbed Lyapunov equation A T X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], but here we focus on a framework where the matrix A has a ...
problem.IfX(t)isasolutionofthisd.e.,thenthedistancebetweenX(t) andAdecreasesastincreases;thisdistancefunctionisaLyapunovfunc- tionforthed.e.IfAhasdistinctpositivesingularvalues(whichisageneric condition)thenthisd.e.hasonlyonestableequilibriumpoint.Theother ...
Based on a dynamical low-rank approximation of the solution, a new splitting integrator is proposed for a quite general class of stiff matrix differential equations. This class comprises differential Lyapunov and differential Riccati equations that arise from spatial discretizations of partial differential...
The first class of matrix equations that we consider are constrained Sylvester equations, which essentially consist of Sylvester's equation along with a constraint on the solution matrix. These therefore constitute a system of matrix equations. The second are generalized Lyapunov equations, which are ...