A global variant of the COCR method for the complex symmetric Sylvester matrix equation AX + XB = C. (15th July 2021)

• Record Type: Journal Article
• Authors: Li, Sheng-Kun; Wang, Mao-Xiao; Liu, Gang
• Is Part Of: Computers & mathematics with applications. Volume 94(2021)
• Page Start: 104
• Page End: 113
• Publication Date: 2021-07-15
• Subjects: Sylvester matrix equation -- Complex symmetric matrix -- Global complex symmetric M-Lanczos process -- Gl-COCR method -- Smoothing technique; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.04.026
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Complex symmetric Sylvester matrix equations appear in many applications, such as the numerical solution of the complex Helmholtz equations. In this paper, by designing a global complex symmetric M -Lanczos process we develop a global variant of the conjugate A -orthogonal conjugate residual method (Gl-COCR) for solving the Sylvester matrix equation A X + X B = C with complex symmetric coefficient matrices. To obtain the smooth and monotone convergence behavior, we also propose a smoothed Gl-COCR method, denoted by SGl-COCR. Finally, numerical examples are given to illustrate the performances of our methods.