Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation

2013 ◽  
Vol 56 (5) ◽  
pp. 967-982 ◽  
Author(s):  
HuaiAn Diao ◽  
XingHua Shi ◽  
YiMin Wei
Keyword(s):  
Small Sample ◽  
Condition Numbers ◽  
Sylvester Equation ◽  
Condition Estimation ◽  
Generalized Sylvester Equation ◽  
Effective Condition

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.

Small-sample statistical condition estimation of rational Riccati equations

2020 ◽  
Vol 103 ◽  
pp. 106172 ◽  
Author(s):  
Liping Zhang ◽  
Eric King-Wah Chu ◽  
Hung-Yuan Fan ◽  
Yimin Wei
Keyword(s):  
Riccati Equations ◽  
Small Sample ◽  
Condition Estimation
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