scholarly journals Numerical solution to low rank perturbed Lyapunov equations by the sign function method

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 723-724
Author(s):  
Peter Benner ◽  
Jonas Denißen
Keyword(s):  
Numerical Solution ◽  
Function Method ◽  
Low Rank ◽  
Lyapunov Equations ◽  
Sign Function

Low-Rank Solution of Lyapunov Equations

SIAM Review ◽  
2004 ◽  
Vol 46 (4) ◽  
pp. 693-713 ◽  
Author(s):  
Jing-Rebecca Li ◽  
Jacob White
Keyword(s):  
Low Rank ◽  
Lyapunov Equations

The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

2021 ◽  
Vol 8 (3) ◽  
pp. 526-536
Author(s):  
L. Sadek ◽  
◽  
H. Talibi Alaoui ◽  
Keyword(s):  
Matrix Equation ◽  
Large Scale ◽  
Krylov Subspace ◽  
Low Rank ◽  
Lyapunov Equations ◽  
Lanczos Algorithm ◽  
Lyapunov Matrix ◽  
Block Lanczos ◽  
Low Dimensional ◽  
Differential Lyapunov Equations

In this paper, we present a new approach for solving large-scale differential Lyapunov equations. The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem. Moreover, we also give some theoretical results. The numerical results demonstrate the performance of our approach.

scholarly journals Inexact methods for the low rank solution to large scale Lyapunov equations

2020 ◽  
Vol 60 (4) ◽  
pp. 1221-1259 ◽  
Author(s):  
Patrick Kürschner ◽  
Melina A. Freitag
Keyword(s):  
Large Scale ◽  
Low Rank ◽  
Lyapunov Equations ◽  
Inexact Methods
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