On Euler preconditioned SHSS iterative method for a class of complex symmetric linear systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 5, pp. 1607-1627.

In this paper, we propose an Euler preconditioned single-step HSS (EP-SHSS) iterative method for solving a broad class of complex symmetric linear systems. The proposed method can be applied not only to the non-singular complex symmetric linear systems but also to the singular ones. The convergence (semi-convergence) properties of the proposed method are carefully discussed under suitable restrictions. Furthermore, we consider the acceleration of the EP-SHSS method by preconditioned Krylov subspace method and discuss the spectral properties of the corresponding preconditioned matrix. Numerical experiments verify the effectiveness of the EP-SHSS method either as a solver or as a preconditioner for solving both non-singular and singular complex symmetric linear systems.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2019029
Classification : 65F10, 65F50, 65F15, 65N22
Mots-clés : Complex symmetric linear systems, Preconditioned EP-SHSS method, convergence, Semi-convergence, Spectral properties
Li, Cheng-Liang 1 ; Ma, Chang-Feng 1

1 
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     author = {Li, Cheng-Liang and Ma, Chang-Feng},
     title = {On {Euler} preconditioned {SHSS} iterative method for a class of complex symmetric linear systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1607--1627},
     publisher = {EDP-Sciences},
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     doi = {10.1051/m2an/2019029},
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Li, Cheng-Liang; Ma, Chang-Feng. On Euler preconditioned SHSS iterative method for a class of complex symmetric linear systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 5, pp. 1607-1627. doi : 10.1051/m2an/2019029. http://www.numdam.org/articles/10.1051/m2an/2019029/

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