Abstract:

The convergence performance of the extrapolated GaussSeidel iterative method and its relationship with H-matrix were discussed. The convergence relationship between the extrapolated GaussSeidel and the Jacobi iterative methods and also the range of the extrapolated parameter when the method
 converges were given. The upper bound estimates for the spectral radius of the extrapolated GaussSeidel iterative method were obtained by using the optimally scaled matrix and the estimator of M^-1N. Meanwhile, equivalent conditions for general Hmatrices based on the extrapolated GaussSeidel and the GaussSeidel iterative methods were provided.

Key words: Hmatrix, GaussSeidel iterative method, extrapolated GaussSeidel iterative method, optimally scaled matrix, spectral radius