Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses
Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses
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DOI：
10.1155/2017/6429725
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发表时间：
2017-06
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影响因子：
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通讯作者：
P. Stanimirović;M. Ciric;I. Stojanovic;Dimitrios Gerontitis
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文献类型：
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作者：
P. Stanimirović;M. Ciric;I. Stojanovic;Dimitrios Gerontitis
给出了-逆、-逆和-逆在范围和/或零空间上满足一定条件的存在条件和表示形式。这些表示适用于复杂矩阵和涉及某些矩阵方程的解。从引入的表示中产生的算法被开发。特别是，这些算法可用于计算Moore-Penrose逆、Drazin逆和通常的矩阵逆。所介绍的算法的实现是在实矩阵集合上定义的，它是基于Simulink实现的GNN模型来求解所涉及的矩阵方程。通过这种方法，我们在求解某些矩阵方程的基础上，开发了生成各种类型的内外广义逆的计算程序。从而在求解矩阵方程问题与广义逆的数值计算问题之间建立了一些新的关系。理论结果适用于复杂矩阵，所开发的算法既适用于时变实矩阵，也适用于时变实矩阵。
Conditions for the existence and representations of -, -, and -inverses which satisfy certain conditions on ranges and/or null spaces are introduced. These representations are applicable to complex matrices and involve solutions of certain matrix equations. Algorithms arising from the introduced representations are developed. Particularly, these algorithms can be used to compute the Moore-Penrose inverse, the Drazin inverse, and the usual matrix inverse. The implementation of introduced algorithms is defined on the set of real matrices and it is based on the Simulink implementation of GNN models for solving the involved matrix equations. In this way, we develop computational procedures which generate various classes of inner and outer generalized inverses on the basis of resolving certain matrix equations. As a consequence, some new relationships between the problem of solving matrix equations and the problem of numerical computation of generalized inverses are established. Theoretical results are applicable to complex matrices and the developed algorithms are applicable to both the time-varying and time-invariant real matrices.