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 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 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

A Note on Generic Kronecker Orbits of Matrix Pencils with Fixed Rank

2008 ◽  
Vol 30 (2) ◽  
pp. 491-496 ◽  
Author(s):  
Fernando De Terán ◽  
Froilán M. Dopico
Keyword(s):  
Matrix Pencils ◽  
Fixed Rank

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

On Wilkinson's problem for matrix pencils

2015 ◽  
Vol 30 ◽  
pp. 632-648 ◽  
Author(s):  
Sk. Ahmad ◽  
Rafikul Alam
Keyword(s):  
Condition Number ◽  
Matrix Pencil ◽  
Upper Bounds ◽  
Regular Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Lower And Upper Bounds ◽  
Matrix Pencils

Suppose that an n-by-n regular matrix pencil A -\lambda B has n distinct eigenvalues. Then determining a defective pencil E−\lambda F which is nearest to A−\lambda B is widely known as Wilkinson’s problem. It is shown that the pencil E −\lambda F can be constructed from eigenvalues and eigenvectors of A −\lambda B when A − \lambda B is unitarily equivalent to a diagonal pencil. Further, in such a case, it is proved that the distance from A −\lambda B to E − \lambdaF is the minimum “gap” between the eigenvalues of A − \lambdaB. As a consequence, lower and upper bounds for the “Wilkinson distance” d(L) from a regular pencil L(\lambda) with distinct eigenvalues to the nearest non-diagonalizable pencil are derived.Furthermore, it is shown that d(L) is almost inversely proportional to the condition number of the most ill-conditioned eigenvalue of L(\lambda).

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