Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices

•Linear system of equations with complex symmetric positive semi-definite coefficient matrices is investigated.•The main idea is based on introducing a new single step iteration scheme for solving this system.•Convergence analysis is give in detail and optimal parameter for new iterative procedure is obtained.•The new scheme is compared with some well-known techniques already proposed in the literature.•Under some conditions, new algorithm converges fast in comparison with CRI, PMHSS and TSCSP methods.•Test problems taken from the literature are solved and simulation results are reported to observe performance of presented scheme. In this study, we propose a new single-step iterative method for solving complex linear systems Az≡(W+iT)z=f, where z,f∈Rn, W∈Rn×n and T∈Rn×n are symmetric positive semi-definite matrices such that null(W)∩null(T)={0}. The convergence of the new method is analyzed in detail and discussion on the obtaining the optimal parameter is given. From Wang et al. (2017)[36] we can write W=PTDWP,T=PTDTP, where DW=Diag(μ1,…,μn),DT=Diag(λ1,…,λn), and P∈Rn×n is a nonsingular matrix and λk, μk satisfy μk+λk=1,0≤λk,μk≤1,k=1,…,n. Then we show that under some conditions on μmax=max{μk}k=1n, the new method has faster convergence rate in comparison with recently introduced methods. Finally, some numerical examples are given to demonstrate the efficiency of the new procedure in actual computation.