Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration

2008 ◽  
Author(s):  
James V. Lambers
Keyword(s):  
Spectral Methods ◽  
Krylov Subspace ◽  
Lanczos Iteration ◽  
Block Lanczos ◽  
Krylov Subspace Spectral Methods

Krylov Subspace Spectral Methods for Systems of Variable-Coefficient PDE

2007 ◽  
Author(s):  
James V. Lambers ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Spectral Methods ◽  
Variable Coefficient ◽  
Krylov Subspace ◽  
Krylov Subspace Spectral Methods

scholarly journals Recent advances in Krylov subspace spectral methods

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020143-2020144
Author(s):  
James V. Lambers
Keyword(s):  
Spectral Methods ◽  
Krylov Subspace ◽  
Recent Advances ◽  
Krylov Subspace Spectral Methods

Application of Block Krylov Subspace Spectral Methods to Maxwell’s Equations

2009 ◽  
Author(s):  
James V. Lambers ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
Li Xu
Keyword(s):  
Spectral Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Krylov Subspace ◽  
Krylov Subspace Spectral Methods

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.

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