scholarly journals Numerical Methods for Large-Scale Lyapunov Equations with Symmetric Banded Data

2018 ◽  
Vol 40 (5) ◽  
pp. A3581-A3608 ◽  
Author(s):  
Davide Palitta ◽  
Valeria Simoncini
Keyword(s):  
Numerical Methods ◽  
Large Scale ◽  
Lyapunov Equations

Numerical Methods for Large-Scale Electronic State Calculation on Supercomputer

2019 ◽  
pp. 15-1-15-16
Author(s):  
Takeo Hoshi ◽  
Yusaku Yamamoto ◽  
Tomohiro Sogabe ◽  
Kohei Shimamura ◽  
Fuyuki Shimojo ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Electronic State ◽  
Large Scale ◽  
State Calculation

scholarly journals Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

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
Sign in / Sign up

Export Citation Format

Share Document