Lanczos算法误差估计的若干问题

Problems concerning error estimate of Lanczos algorithm

设Ａ为ｎＸｎ实对称矩阵，对于给定的ｊ个线性无关列向量组成的ｎ×ｊ实矩阵Ｑ，对任意ｊ×ｊ实矩阵Ｔ，记Ｒ（Ｔ）＝ＡＱ－ＱＴ。本文给出ｊ×ｊ实矩陈Ｈ，使｜｜Ｒ（Ｈ），并证明当Ｔ取矩阵Ｈ时，文献［１］中Ｐ．１２２定理４．１０的“”可以改变成“１”。

Let A be an nxn real symmetricmatrix. Suppose an nxj real matrix Q is com- posed of linearity-independent column vectors in a given number of j . For any jxj real matrix T , set R(T) =AQ -- QT . In this paper , a jxj real matrix H is found to be such that R(H)=min (T) Moreover, we have proved that the ' ' of theorem 4. 10 in [1] can be subtituted by ' 1' .