摘要
针对Gauss-Seidel迭代法求解大型线性方程组Ax=b时,结合矩阵分裂理论及比较定理,给方程两边同时左乘非奇异矩阵P(也称为预条件矩阵),对新的系数矩阵PA进行矩阵分裂时,引入参数α,以使矩阵分裂更加一般化,说明这种方法不仅能加速Gauss-Seidel迭代法的收敛,而且优于一般的预条件方法。最后给出一个数值例子。
The Gauss-Seidel iterative method is discussed to solve the large linear system Ax=b by using matrix iterative analysis and comparison theorems,make the nonsingular matrix P（ preconditioned matrix ）to left multiply the linear system two-sided.The parameter α is pull in to splitting the new coefficient matix,then prove the improved method not only to accelerate the Gauss-Seidel iterative method,but also to excel the general preconditioned method.Last the numerical example is given.
出处
《科学技术与工程》
2010年第27期6610-6613,共4页
Science Technology and Engineering
基金
宝鸡文理学院重点项目基金(ZK09126)资助
