scholarly journals Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations

2019 ◽  
Vol 40 (2) ◽  
pp. 440-453 ◽  
Author(s):  
Itziar Baragan͂a ◽  
Alicia Roca
Keyword(s):  
Low Rank ◽  
Regular Matrix ◽  
Matrix Pencils

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 Fixed rank perturbations of regular matrix pencils

2020 ◽  
Vol 589 ◽  
pp. 201-221
Author(s):  
Itziar Baragaña ◽  
Alicia Roca
Keyword(s):  
Regular Matrix ◽  
Matrix Pencils ◽  
Fixed Rank

A deflation method for regular matrix pencils

2011 ◽  
Vol 218 (6) ◽  
pp. 2913-2920
Author(s):  
Edgar Pereira ◽  
Cecilia Rosa
Keyword(s):  
Regular Matrix ◽  
Matrix Pencils

Balancing Regular Matrix Pencils

2006 ◽  
Vol 28 (1) ◽  
pp. 253-263 ◽  
Author(s):  
Damien Lemonnier ◽  
Paul Van Dooren
Keyword(s):  
Regular Matrix ◽  
Matrix Pencils

scholarly journals Stability of invariant subspaces of regular matrix pencils

1995 ◽  
Vol 221 ◽  
pp. 219-226 ◽  
Author(s):  
Juan M. Gracia ◽  
Francisco E. Velasco
Keyword(s):  
Invariant Subspaces ◽  
Regular Matrix ◽  
Matrix Pencils
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