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

Akbar Shirilord and Mehdi Dehghan

Applied Mathematics and Computation, 2022, vol. 426, issue C

Abstract: 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.

Keywords: Single step iterative method; Optimal parameter; Complex matrix; Symmetric positive semi-definite matrix; Convergence (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:426:y:2022:i:c:s0096300322001953

DOI: 10.1016/j.amc.2022.127111

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