The Unified Frame of Alternating Direction Method of Multipliers for Three Classes of Matrix Equations Arising in Control Theory

Ke, Youqi; Ma, Changfeng

doi:10.1002/asjc.1560

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2019

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Cited by 4 publications

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“…It is well known that linear matrix equations play crucial roles in engineering and applied mathematics (Ke and Ma, 2018; Simoncini, 2016). For example, the Stein matrix equation…”

Section: Introductionmentioning

confidence: 99%

Partially doubly symmetric solutions of general Sylvester matrix equations

Hajarian

2019

Transactions of the Institute of Measurement and Control

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The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to design the Hestenes-Stiefel (HS) version of biconjugate residual (Bi-CR) algorithm for computing the (least Frobenius norm) partially doubly symmetric solution [Formula: see text] of the general Sylvester matrix equations [Formula: see text] for [Formula: see text]. We show that the proposed algorithm converges in a finite number of iterations. Finally, numerical results compare the proposed algorithm to alternative algorithms.

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“…It is well known that linear matrix equations play crucial roles in engineering and applied mathematics (Ke and Ma, 2018; Simoncini, 2016). For example, the Stein matrix equation…”

Section: Introductionmentioning

confidence: 99%