【摘要】 设 Ａ是对称正定矩阵，λ₁是 Ａ 的最大或最小特征值，χ₁是对应的特征向量．｛zk｝是用共轭斜量法求解方程组 Αχ＝ｂ时的近似解序列，ｅi＝Ａ～（₁）b-zi,本文给出了|x₁～Tei|较合理的上界估计式。从而为分析预处理共轭斜量法提供了进一步的理论基础。更多还原

【Abstract】 LetA be a positive definite matrix, λ₁ is a largest or smallest eigenvalue of A, x_l is the corresponding eigenvector. Let the method of conjugate gradient be applied to the solution of the linear system Ax=b producing a sequence of iterat- es z_o, z_l, … and an associated sequence of eigenvectors e_i =A～（-1）b-z_i. In this paper, the bounds of |x₁～He_i| are obtained, and they are independent of the condition number of A. The result of the paper will do good to the analysis of the Conju- gate gradient method.更多还原