<正> 引 言 矩阵的求逆条件数是它关于求逆或广义逆病态程度的度量;从另外角度看,实际上也是矩阵列向量(或行向量)最大无关组相关程度或它接近更低秩矩阵程度的度量。 通常用的条件数有某些缺点。首先,估计这些条件数涉及计算A~(-1)或A~+或A的奇异值,代价很高,其次,它们用于线性代数方程组摄动解的误差估计时往往出现严重高估。 本文提出了新的条件数,它们克服了上述缺点又具有与谱条件数相类似的好性质,同时还对谱点的分布有所反映。 先将一个要用到的定理陈述如下: 平均值定理若λ_1>0,i=1,2,…,n,则

The condition numbers usually used with respect to inversion for matrix possess some defects. Firstly, the evaluations of these condition numbers require calculating inverses or generalized inverses or singular values of the matrix, causing great cost. Secondly, the error estimates of perturbation solutions are often too high because of the use of these numbers.In this article, several new condition numbers are suggested, which can not only overcome the defects mentioned above, but also possess the same properties as the spectral condition number, and moreover, reflect the distribution of spectral points to some extent.