Preprint No. MPIMD/12-15

Title: On the Squared Smith Method for Large-Scale Stein Equations

Author(s): Peter Benner, Grece El Khoury, Miloud Sadkane


Date: 2012-09-11


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.


author = {Peter Benner and Grece El Khoury and Miloud Sadkane},
title = {On the Squared Smith Method for Large-Scale Stein Equations},
number = {MPIMD/12-15},
month = sep,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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