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Factorized squared Smith method for large-scale Stein equations with high-rank terms
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DOI：10.1016/j.automatica.2023.111057.png)
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Solving large-scale Stein equations with high-ranked coefficient and constant terms is relatively difficult since the solution is no longer numerically low-ranked and its storage and outputting are nontrivial. This paper presents a factorized squared Smith method (FSS) that consists of banded and low-ranked parts to overcome this obstacle when the coefficient and the constant matrices are banded-plus-low-ranked. The deflation process as well as the partial truncation and compression are presented to control the growth of the columns of the low-ranked factors, effectively reducing the complexity of the FSS method. The convergence of the banded and the low-ranked parts is established and the banded part is shown being always numerically banded under some assumptions. The residual computation as well as the termination condition have been redesigned. Numerical examples indicate that for large-scale problems, the proposed FSS algorithm outperforms the Smith method with hierarchical HODLR structured toolkit on CPU time.(c) 2023 Published by Elsevier Ltd.
Keyword:
Large-scale Stein equations
Smith method
Iteration scheme
期刊
IF:
5.9
论文数:
1.2W
被引数:
5.2W
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