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The conjugate gradient methods for solving the generalized periodic Sylvester matrix equations

  • Min SunEmail author
  • Yiju Wang
Original Research
  • 72 Downloads

Abstract

This work is devoted to designing two conjugate gradient methods for the least Frobenius norm solution of the generalized periodic Sylvester matrix equations. When the studied problem is consistent, the first conjugate gradient method can find its solution within finite iterative steps in the absence of round-off errors. Furthermore, its least Frobenius norm solution can be obtained with some special kind of initial matrices. When the studied problem is inconsistent, the second conjugate gradient method with some special kind of initial matrices can find its least squares solution with the least Frobenius norm within finite iterative steps in the absence of round-off errors. Finally, several numerical examples are tested to validate the performance of the proposed methods.

Keywords

The conjugate gradient method The generalized periodic Sylvester matrix equations Finite convergence 

Mathematics Subject Classification

90C25 94A08 

Notes

Acknowledgements

The authors gratefully acknowledge the valuable comments of the editor and the anonymous reviewers. This work is supported by the National Natural Science Foundation of China (Nos. 11671228, 11601475), the foundation of National Natural Science Foundation of Shandong Province (No. ZR2016AL05), Scientific Research Project of Shandong Universities (No. J15LI11).

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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZaozhuang UniversityZaozhuangPeople’s Republic of China
  2. 2.School of ManagementQufu Normal UniversityQufuPeople’s Republic of China

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