Premium
On the squared Smith method for large‐scale Stein equations
Author(s) -
Benner Peter,
Khoury Grece El,
Sadkane Miloud
Publication year - 2014
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1918
Subject(s) - mathematics , convergence (economics) , rank (graph theory) , scale (ratio) , mean squared error , statistics , combinatorics , physics , quantum mechanics , economics , economic growth
SUMMARY A squared Smith type algorithm for solving large‐scale discrete‐time Stein equations is developed. The algorithm uses restarted Krylov spaces to compute approximations of the squared Smith iterations in low‐rank factored form. Fast convergence results when very few iterations of the alternating direction implicit method are applied to the Stein equation beforehand. The convergence of the algorithm is discussed and its performance is demonstrated by several test examples. Copyright © 2013 John Wiley & Sons, Ltd.