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Article

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

by
Bo Yu
,
Ning Dong
* and
Baiquan Hu
School of Science, Hunan University of Technology, Zhuzhou 412007, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(4), 249; https://doi.org/10.3390/axioms13040249
Submission received: 9 March 2024 / Revised: 3 April 2024 / Accepted: 5 April 2024 / Published: 10 April 2024
(This article belongs to the Special Issue The Numerical Analysis and Its Application)
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Abstract

Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended to a low-rank structured format, and the error of the algorithm is analyzed. Numerical experiments demonstrate that the operator Smith iteration outperforms existing linearly convergent iterative methods in terms of computation time and accuracy. The low-rank structured iterative format is highly effective in approximating the solutions of large-scale structured problems.
Keywords: coupled Stein equations; operator Smith algorithm; jump control system; low rank; large-scale problems coupled Stein equations; operator Smith algorithm; jump control system; low rank; large-scale problems

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MDPI and ACS Style

Yu, B.; Dong, N.; Hu, B. Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems. Axioms 2024, 13, 249. https://doi.org/10.3390/axioms13040249

AMA Style

Yu B, Dong N, Hu B. Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems. Axioms. 2024; 13(4):249. https://doi.org/10.3390/axioms13040249

Chicago/Turabian Style

Yu, Bo, Ning Dong, and Baiquan Hu. 2024. "Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems" Axioms 13, no. 4: 249. https://doi.org/10.3390/axioms13040249

APA Style

Yu, B., Dong, N., & Hu, B. (2024). Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems. Axioms, 13(4), 249. https://doi.org/10.3390/axioms13040249

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