期刊论文

Liu, Zhongyun

英文

Numerical Linear Algebra with Applications

1070-5325

2020

27

5

e2320-

10.1002/nla.2320

The authors are grateful to the anonymous referees for their valuable comments and suggestions which improved the quality of this paper. Also, The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the Hunan Key Laboratory of mathematical modeling and analysis in engineering, the Portuguese Funds through FCT‐Fundaco para a Cincia, within the Project UIDB/00013/2020 and UIDP/00013/2020. This work does not have any conflicts of interest. The authors are grateful to the anonymous referees for their valuable comments and suggestions which improved the quality of this paper. Also, The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the Hunan Key Laboratory of mathematical modeling and analysis in engineering, the Portuguese Funds through FCT-Fundac?o para a Ci?ncia, within the Project UIDB/00013/2020 and UIDP/00013/2020. This work does not have any conflicts of interest.

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In this paper, we study the alternating direction implicit (ADI) iteration for solving the continuous Sylvester equation AX + XB = C, where the coefficient matrices A and B are assumed to be positive semi-definite matrices (not necessarily Hermitian), and at least one of them to be positive definite. We first analyze the convergence of the ADI iteration for solving such a class of Sylvester equations, then derive an upper bound for the contraction factor of this ADI iteration. To reduce its computational complexity, we further propose an inexac...