An improvement of H. Wang preconditioner for L-matrices


  • Hamideh Nasabzadeh Bojnord University ,Iran





Linear system, AOR method, Jacobi method, Gauss-Seidel method, Spectral radius, M-matrix, L-matrix, Preconditioner


In this paper, we improve the preconditioner, that introduced by H. Wang et al [6]. The H. Wang preconditioner \(P\in R^{n\times n}\) has only one non-zero, non-diagonal element in \(P_{n1}\) or \(P_{1n}\) , when \(a_{1n}a_{n1}\ne 0\) . But the new preconditioner has only one non-zero, non-diagonal element in  \(P_{ij}\) or  \(P_{ji}\) if \(a_{ij}a_{ji}\ne 0\), so the H. Wang preconditioner is a spacial case of the new preconditioner for L-matrices. Also we present two models to construct a better \(I+S\) type preconditioner for the   \(AOR\) iterative method. Convergence analysis are given, numerical results are presented which show the effectiveness of the new preconditioners.


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