Preconditioned symmetric block triangular splitting iteration method for a class of complex symmetric linear systems

On symmetric block triangular splitting iteration method for a class of complex symmetric system of linear equations

“…That is Remark 1. From the above result and Theorem 2 in [30], the SSTS iteation method has a larger convergent domain than PSBTS iteration method for parameter α and it is insensitive to parameter ω. Thus, our method will be more robust than the PSBTS iteation method to solve linear system (1.1).…”

“…Remark 2. For the SSTS and the PSBTS iteration methods, we observe that they have the same optimal convergence factor according to the above theorem and Theorem 3 in [30]. The PSBTS iteration method need solving four sub-systems with coefficient matrix W ω , but our method only need dealing with two subsystems with respect to W ω .…”

“…Expect for the MHSS iteration method, the parameters for tested methods are the theoretical optimal ones. The parameter of the SBTS, PGSOR and PSBTS iteration methods are chosen according to Theorem 3.5 in [29], Theorem 2.4 in [27] and Theorems 3 and 4 in [30], respectively. In terms of the SSTS iteration method, we choose the theoretical optimal ones by the Theorem 3.6 and also provide the experiential optimal ones at the same time.…”

“…Very recently, Li et al [29] established a symmetric block triangular splitting (SBTS) iteration method to linear system (1.1) based on a triangular splitting method for saddle point problems. Then a preconditioned SBTS(PSBTS) iteration method was designed by Zhang et al [30] and the performance of PSBTS iteration method is outstanding than the SBTS one under some restrictions.…”

A new double-step splitting iteration method for certain block two-by-two linear systems

“…Liang and Zhang (2016) derived the symmetric SOR (SSOR) iteration method for (1) and studied its optimal parameter. Besides, a symmetric block triangular splitting (SBTS) iteration method and its preconditioned version were developed in Li et al (2018) and Zhang et al (2018), respectively. Recently, Liang and Zhang (2019) introduced the additive block triangular (ABT) method for (1).…”