Abstract This paper is a study on main properties and characterizations of the DMP inverse. Also, corresponding representations and computational procedures are derived. Particularly, an upgrade of the bordering method to the case of the DMP inverse is considered as well as applications of the DMP inverse in solving singular linear systems. Also, the DMP inverse of an upper block triangular matrix and its sign pattern are investigated. Furthermore, several computational procedures aimed to approximating the DMP inverse are developed, implemented and tested. The main of them are the limit representation, a revised successive matrix squaring iterations and the Gradient Neural Network (GNN) dynamical system. Finally, some perturbation bounds and continuity of the DMP inverse are studied.

中文翻译：

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DMP 逆的表征、迭代方法、符号模式和扰动分析及其应用

摘要 本文研究了DMP逆的主要性质和特征。此外，还导出了相应的表示和计算程序。特别地，考虑了边界方法对DMP逆情况的升级以及DMP逆在求解奇异线性系统中的应用。此外，还研究了上块三角矩阵的 DMP 逆及其符号模式。此外，开发、实施和测试了几个旨在逼近 DMP 逆的计算程序。其中主要是极限表示、修正的连续矩阵平方迭代和梯度神经网络 (GNN) 动态系统。最后，研究了 DMP 逆的一些扰动边界和连续性。