@article{Li2022, 
author = {Qian Li and Qianqian Yuan and Jianhua Chen},
title = {An efficient relaxed shift-splitting preconditioner for a class of complex symmetric indefinite linear systems},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {17123-17132},
keywords = {symmetric indefinite systems, scalar matrix, ERSS preconditioner, parameter value, Frobenius norm},
url = {https://www.sciopen.com/article/10.3934/math.2022942},
doi = {10.3934/math.2022942},
abstract = {In this work, by introducing a scalar matrix    α  I, we transform the complex symmetric indefinite linear systems    (  W  +  i  T  )  x  =  b into a block two-by-two complex equations equivalently, and propose an efficient relaxed shift-splitting (ERSS) preconditioner. By adopting the relaxation technique, the ERSS preconditioner is not only a computational advantage but also closer to the original two-by-two of complex coefficient matrix. The eigenvalue distributions of the preconditioned matrix are analysed. An efficient and practical formula for computing the parameter value    α is also derived by computing the Frobenius norm of symmetric indefinite matrix    T. Numerical examples on a few model problems are illustrated to verify the performances of the ERSS preconditioner.}
}