Geodesic
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
Applications of Mathematics, Tome 69 (2024) no. 3, pp. 311-337 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We multiply both sides of the complex symmetric linear system $Ax=b$ by $1-{\rm i}\omega $ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.
We multiply both sides of the complex symmetric linear system $Ax=b$ by $1-{\rm i}\omega $ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.
DOI : 10.21136/AM.2024.0133-23
Classification : 65F10, 65H10
Keywords: DDSS iteration method; linear equations; SPD matrix; SPSD matrix; convergence property 
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     title = {A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations},
     journal = {Applications of Mathematics},
     pages = {311--337},
     year = {2024},
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Li, Beibei; Cui, Jingjing; Huang, Zhengge; Xie, Xiaofeng. A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations. Applications of Mathematics, Tome 69 (2024) no. 3, pp. 311-337. doi: 10.21136/AM.2024.0133-23

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