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中文摘要：
讨论了新的预条件矩阵下的预条件Gauss-Seidel法.在更广义的分裂条件下,将此法应用于H-矩阵及其比较矩阵上,并得到了相应的收敛结果和谱半径的比较结果,从而说明应用于H-矩阵的预条件Gauss-Seidel法的收敛速度要比应用于它的比较矩阵的预条件Gauss-Seidel法的收敛速度快.最后,给出一个数值例子验证得到的结果.
英文摘要：
Under a new preconditioned matrix,the preconditioned Gauss-Seidel method is discussed.In a more general split conditions,this method is applied to H-matrix and its comparison matrix,the corresponding convergence results and the comparison results of the spectral radius are obtained.This shows that the convergence rate of the preconditioned Gauss-Seidel method corresponding to H-matrix is faster than that of the preconditioned Gauss-Seidel method corresponding to its comparison matrix.Finally,a numerical example is also given to illustrate the results.
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