Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices. (English) Zbl 0966.65032
The authors discuss the iterative solution of linear systems by modified Gauss-Seidel (MGS) type methods and modified Jacobi (MJ) type methods. The convergence of these algorithms is analyzed and many properties for a matrix splitting of the coefficient matrix of the system are presented. Some recent results are improved.
The main tool for a comparison of the different Gauss-Seidel type methods used by the authors is the spectral radius of the iteration matrix of the method. The authors prove that if the coefficient matrix of the system is a non-singular M-matrix, the MGS method converges for all parameters in \([0,1]\) and the convergence rates are better than those of the corresponding Gauss-Seidel type methods. No numerical experiments.
The main tool for a comparison of the different Gauss-Seidel type methods used by the authors is the spectral radius of the iteration matrix of the method. The authors prove that if the coefficient matrix of the system is a non-singular M-matrix, the MGS method converges for all parameters in \([0,1]\) and the convergence rates are better than those of the corresponding Gauss-Seidel type methods. No numerical experiments.
Reviewer: Iulian Coroian (Baia Mare)
MSC:
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
Keywords:
Z-matrices; modified Gauss-Seidel type method; modified Jacobi type method; convergence; spectral radius; algorithms; matrix splitting; M-matrixReferences:
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