摘要
1 共轭梯度法 1952年M·R·Hestenes和E.Stiefel从极小化的观点来讨论代数方程组Ax=b的解,给出了著名的共轭梯度法(Conjugate Gradient,简称CG).若A是N阶对称正定实矩阵,记向量x和y的内积为(x,y)。
Since 1977 a mighty advance has been made to preconditioned conjugate gradient (PCG) such that PCG becomes a most important method for solving linear algebraic systems. It has a superlinear convergence rate and a vectorizable algorithm. Especially, PCG is suited to solve problems of a very large sparse matrix. The purpose of this paper is to introduce briefly main results and general situation of its history over past ten years. The new trends and some of the new advances are also surveyed.
出处
《数学进展》
CSCD
北大核心
1992年第2期129-139,共11页
Advances in Mathematics（China）
