Perturbation bounds of generalized inverses

作者：Meng, Lingsheng; Zheng, Bing^*; Ma, Peilan

来源：Applied Mathematics and Computation, 2017, 296: 88-100.

DOI：10.1016/j.amc.2016.10.017

• Generalized inverses
• Additive perturbation bound
• Multiplicative perturbation bound
• Distance
• Optimality

Let complex matrices A and B have the same sizes. We characterize the generalized inverse matrix B-(1,B-i), called an {1, i}-inverse of B for each i = 3 and 4, such that the distance between a given (1, i}-inverse of a matrix A and the set of all {1, i}-inverses of the matrix B reaches minimum under 2-norm (spectral norm) and Frobenius norm. Similar problems are also studied for {1, 2, i}-inverse. In practice, the matrix B is often considered as the perturbed matrix of A, and hence based on the previous results, the additive perturbation bounds for the {l, i}- and {1, 2, i}-inverses and multiplicative perturbation bounds for the {1}-, {1, i}- and {1, 2, i}-inverses are proposed. Numerical examples show that these multiplicative perturbation bounds can be achieved respective under 2-norm and Frobenius norm.

• 出版日期2017-3-1
• 单位伊犁师范大学; 兰州大学