On unique solvability of the piecewise linear equation system

Shubham Kumar; Deepmala

doi:10.33993/jnaat512-1271

Authors

Shubham Kumar Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, India
Deepmala Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, India

DOI:

https://doi.org/10.33993/jnaat512-1271

Keywords:

Unique solvability, Absolute value equations, Linear complementarity problem

Abstract views: 232

Abstract

In this article, we take the piecewise linear equation system \(x-W|x|=b\), which is also known by absolute value equation, where \(W\in {\mathbb R}^ {n\times n}\), \(b\in {\mathbb R}^{n}\) are given and to undetermined the value of \(x\in {\mathbb R}^{n}\). The absolute value equation (AVE) has many applications in various fields of mathematics like bi-matrix games, linear interval systems, linear complementarity problems (LCP) etc. By the equivalence relation of AVE with LCP, some necessary and sufficient conditions proved the existence and unique solvability of the AVE. Some examples are also provided to highlight the current singular value conditions for a unique solution that may revise in the future.

(small corrections operated in the pdf file on January 7, 2023)

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