On the squared Smith method for large‐scale Stein equations |
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| Authors: | Peter Benner Grece El Khoury Miloud Sadkane |
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| Institution: | 1. Max Planck Institute for Dynamics of Complex Technical Systems, , 39106 Magdeburg, Germany;2. Laboratoire de Mathématiques de Bretagne Atlantique, Université de Brest, CNRS ‐ UMR 6205, , 29238 Brest Cedex 3, France |
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| Abstract: | 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. |
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| Keywords: | Stein equation squared Smith iteration block Arnoldi low‐rank factor ADI iteration |
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