奇异情形下的结构化扰动(英文)

Structured perturbations in singular case

最近Rump S. M.研究了在范数意义下的结构化扰动问题,即对求解线性方程组的条件数和矩阵求逆的条件数作了探讨,并且刻画了非奇异矩阵到奇异矩阵的最小距离.把其部分结果推广到奇异情形,即对一类有特定右端项的值域对称的奇异线性方程组,给出了其条件数的不同表示和估计,同时讨论了求矩阵广义逆的条件数.

Recently Rump [2]studies the condition number of linear systems, the condition number of matrix inverse, and the distance to the nearest singular matrix, all problems with respect to normwise structured perturbations. Some of his results are extended to singular case, that is for the range-Hermitian singular linear systems with speci?c right hand sides, and various explicit formulas and estimations for the condition numbers of them are given. Some results for the condition number of generalized inverse are obtained.