首页|Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices
Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices
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NSTL
Elsevier
In this study, we propose a new single-step iterative method for solving complex linear systems Az = (W + iT)z = f, where z, f is an element of R-n, W is an element of R-nxn and T is an element of R-nxn are symmetric positive semi-definite matrices such that null(W) & cap;& nbsp; 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 = (PDWP)-D-T, T = (PDTP)-D-T, where D-W = Diag(mu(1), . . . , mu(n)) , D-T = Diag(lambda(1) , . . . , lambda(n)), and P is an element of R-nxn is a nonsingular matrix and lambda(k) , mu(k )satisfy mu(k )+ lambda(k) = 1 , 0 <= lambda(k), mu(k) <= 1 , k = 1 , . . . , n. Then we show that under some conditions on mu(max) = max{ mu(k)}(n)(k & nbsp;=1) , 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. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
Single step iterative methodOptimal parameterComplex matrixSymmetric positive semi-definite matrixConvergenceALGORITHMS
NSTL
Elsevier
