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

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  • Shirilord, Akbar
  • Dehghan, Mehdi

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.

Suggested Citation

  • Shirilord, Akbar & Dehghan, Mehdi, 2022. "Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    • Handle: RePEc:eee:apmaco:v:426:y:2022:i:c:s0096300322001953
    DOI: 10.1016/j.amc.2022.127111
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