scholarly journals On estimating the separation between (A,B) and (C,D) associated with the generalized Sylvester equation AXD−BXC=E

2018 ◽  
Vol 330 ◽  
pp. 128-140
Author(s):  
Xiao Shan Chen ◽  
Peng Lv
Keyword(s):  
Sylvester Equation ◽  
Generalized Sylvester Equation

A Newton-like method for computing deflating subspaces

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko ◽  
Miloud Sadkane
Keyword(s):  
Stability Problem ◽  
Initial Guess ◽  
Sylvester Equation ◽  
Gmres Method ◽  
Regular Matrix ◽  
Subspace Iteration ◽  
Generalized Sylvester Equation ◽  
Matrix Pencils ◽  
Deflating Subspaces ◽  
Preconditioned Gmres

AbstractThis work is devoted to computations of deflating subspaces associated with separated groups of finite eigenvalues near specified shifts of large regular matrix pencils. The proposed method is a combination of inexact inverse subspace iteration and Newton’s method. The first one is slow but reliably convergent starting with almost an arbitrary initial subspace and it is used as a preprocessing to obtain a good initial guess for the second method which is fast but only locally convergent. The Newton method necessitates at each iteration the solution of a generalized Sylvester equation and for this task an iterative algorithm based on the preconditioned GMRES method is devised. Numerical properties of the proposed combination are illustrated with a typical hydrodynamic stability problem.

A symmetric preserving iterative method for generalized Sylvester equation

2010 ◽  
Vol 13 (3) ◽  
pp. 408-417 ◽  
Author(s):  
Jiao-Fen Li ◽  
Xi-Yan Hu ◽  
Xue-Feng Duan
Keyword(s):  
Iterative Method ◽  
Sylvester Equation ◽  
Generalized Sylvester Equation

scholarly journals THE GENERALIZED SYLVESTER MATRIX EQUATION, RANK MINIMIZATION AND ROTH’S EQUIVALENCE THEOREM

2011 ◽  
Vol 84 (3) ◽  
pp. 441-443 ◽  
Author(s):  
MINGHUA LIN ◽  
HARALD K. WIMMER
Keyword(s):  
Matrix Equation ◽  
Equivalence Theorem ◽  
Sylvester Equation ◽  
Sylvester Matrix Equation ◽  
Rank Minimization ◽  
Sylvester Matrix ◽  
Generalized Sylvester Matrix Equation ◽  
Generalized Sylvester Equation ◽  
Special Case

AbstractRoth’s theorem on the consistency of the generalized Sylvester equationAX−YB=Cis a special case of a rank minimization theorem.

scholarly journals Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hongcai Yin ◽  
Huamin Zhang
Keyword(s):  
Exact Solution ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Iterative Solution ◽  
Sylvester Equation ◽  
Matrix Equations ◽  
Convergence Factor ◽  
The Matrix ◽  
Generalized Sylvester Equation ◽  
Sylvester Matrix Equations

By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equationsAX+YB=CandDX+YE=Fin this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equationAXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.

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