On the nearest stable $ 2\times 2 $ matrix, dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas

Yueh-Cheng Kuo; Huan-Chang Cheng; Jhih-You Syu; Shih-Feng Shieh

doi:10.3934/dcdsb.2020358

Article Contents

2021, Volume 26, Issue 4: 2025-2035. Doi: 10.3934/dcdsb.2020358

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On the nearest stable $ 2\times 2 $ matrix, dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas

1.
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811, Taiwan
2.
Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan

^* Corresponding author: Shih-Feng Shieh
^* Corresponding author: Shih-Feng Shieh

Received: July 31, 2020

Revised: September 30, 2020

Early access: December 2020

Published: April 2021

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Abstract

In this paper, we study the continuous-time nearest stable matrix problem: given a $ 2\times 2 $ real matrix $ A $, minimize the Frobenius norm of $ A-X $, where $ X $ is a stable matrix. We provide an explicit formula for the global minimizer $ X_* $. The uniqueness of the minimizer is also studied.

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Mathematics Subject Classification: 15A39, 15A60.

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References

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