Abstract
For solving a class of complex symmetric linear systems, we introduce a new single-step iteration method, which can be taken as a fixed-point iteration adding the asymptotical error (FPAE). In order to accelerate the convergence, we further develop the parameterized variant of the FPAE (PFPAE) iteration method. Each iteration of the FPAE and the PFPAE methods requires the solution of only one linear system with a real symmetric positive definite coefficient matrix. Under suitable conditions, we derive the spectral radius of the FPAE and the PFPAE iteration matrices, and discuss the quasi-optimal parameters which minimize the above spectral radius. Numerical tests support the contention that the PFPAE iteration method has comparable advantage over some other commonly used iteration methods, particularly when the experimental optimal parameters are not used.
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This work is supported by NNSF with Nos. 11461046, 61563033, and 11401293, NSF of Jiangxi Province with Nos. 20161ACB21005 and 20151BAB201009, and the Scientific Research Foundation of Graduate School of Nanchang University with Nos. YC2015-S018 and CX2016143.
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Xiao, X.Y., Wang, X. A new single-step iteration method for solving complex symmetric linear systems. Numer Algor 78, 643–660 (2018). https://doi.org/10.1007/s11075-017-0393-y
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DOI: https://doi.org/10.1007/s11075-017-0393-y