关于非奇H矩阵某些迭代的谱半径

On Spectral Radius of Some Iterations Regarding Nonsingular H-Matrix

当系数矩阵A是非奇H矩阵时,通过分析求解线性方程组的雅可比、高斯塞德尔和超松弛方法的迭代矩阵特征值,得出相关谱半径的性质,进而将雅可比迭代和高斯塞德尔迭代收敛的充分条件由A为严格对角占优矩阵放宽到A为非奇H矩阵,同时证明了此时低松弛迭代也是收敛的.

When coefficient matrix A is a nonsingular H-matrix, by way of analyzing and determining the Jacobi-, Gauss- Seidel- and SOR- iterative matrix eigenvalues of linear system of equations, the properties of the relevant spectral radius are thus obtained, which thus makes it possible to change the sufficient condition for Jacobi and Gauss-Seidel iterative convergence with A being a strictly diagonally dominant matrix, into the less strict condition of A being a nonsingular H-matrix. And it is proved that the under-relaxation iteration is also convergent under such a condition.