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

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.

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.

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