Two fast algorithms for finding the solution of the lower Hessenberg quasi-Toeplitz linear system from Markov chain.

Yaru Fu, Xiaoyu Jiang, Yanpeng Zheng, Zhaolin Jiang

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Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Yaru FuSchool of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, China.

Xiaoyu JiangSchool of Information Science and Engineering, Linyi University, Linyi, 276000, China. jxy19890422@sina.com.

Yanpeng ZhengSchool of Automation and Electrical Engineering, Linyi University, Linyi, 276000, China. zhengyanpeng0702@sina.com.

Zhaolin JiangSchool of Mathematics and Statistics, Linyi University, Linyi, 276000, China.

Funding

Fundamental Research Program of Shanxi Province 202203021212189National Natural Science Foundation of China 12101284Research Project Supported by Shanxi Scholarship Council of China 2022-169

6 · The paper itself

Abstract

We present two fast algorithms for finding the solution of the nonsingular lower Hessenberg quasi-Toeplitz linear system stem from Markov chain. And we confirm the complexity of these two algorithms is both O[Formula: see text] based on the fact that a lower Hessenberg quasi-Toeplitz matrix can be written as the sum of a Toeplitz matrix and a rank-one matrix, such that the fast solver involves O[Formula: see text] operators for solving the Toeplitz linear system can be adopted. Finally, numerical results prove the superiority and accuracy of our algorithms by comparing the values of residual and CPU time with existing algorithms.

Indexed as

Lower Hessenberg quasi-Toeplitz linear systemLow rank matrixMarkov chainSherman–Morrison–WoodburyToeplitz matrix

Identifiers

PMID40596469

DOI10.1038/s41598-025-06791-3

PMCPMC12215781

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