Our contribution is the development of novel representations and investigations of main properties of the MPCEP inverse. Precisely, we present representations of the MPCEP inverse which involve appropriate Moore–Penrose inverses, projections and full-rank decompositions, as well as limit and integral representations. Determinantal representations for the MPCEP inverse are also established. We study perturbation formulae with perturbation bounds of MPCEP inverse. An equivalent condition for the continuity of the MPCEP inverse is proposed. The MPCEP inverse of a suitable upper block triangular matrix is given. The successive matrix squaring algorithm and splitting method for computing the MPCEP inverse are presented. Some appropriate constrained systems of linear equations are solved applying the MPCEP inverse.

我们的贡献是开发了新颖的表示形式并研究了MPCEP逆的主要性质。准确地说，我们给出了MPCEP逆的表示形式，其中涉及适当的Moore-Penrose逆，投影和满秩分解，以及极限和积分表示。还建立了MPCEP逆的行列式表示。我们研究具有MPCEP逆的摄动范围的摄动公式。提出了MPCEP逆的连续性的等价条件。给出了合适的上块三角矩阵的MPCEP逆。提出了用于计算MPCEP逆的连续矩阵平方算法和分割方法。应用MPCEP逆解了一些合适的线性方程组。