On convergence of a sketch-and-project method for the matrix equation AXB=C

In this paper, based on Lagrangian functions of the optimization problem we develop a sketch-and-project method for solving the linear matrix equation A X B = C by introducing three parameters. A thorough convergence analysis on the proposed method is explored in details. A lower bound on the conver...

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Bibliographic Details
Published in:Computational & applied mathematics 2024, Vol.43 (6), Article 325
Main Authors: Bao, Wendi, Guo, Zhiwei, Li, Weiguo, Lv, Ying
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Convergence
Lagrangian function
Lower bounds
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Parameters
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Summary:In this paper, based on Lagrangian functions of the optimization problem we develop a sketch-and-project method for solving the linear matrix equation A X B = C by introducing three parameters. A thorough convergence analysis on the proposed method is explored in details. A lower bound on the convergence rate and some convergence conditions are derived. By varying three parameters in the new method and convergence theorems, an array of well-known algorithms and their convergence results are recovered. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-024-02847-8