Complementarity Problem With Nekrasov $Z$ tensor

TL;DR

This paper introduces Nekrasov Z tensors, a new tensor class related to P-tensors, and explores their properties and transformations to diagonally dominant tensors within the tensor complementarity problem framework.

Contribution

It defines Nekrasov Z tensors, shows their relation to P-tensors, and proposes a method to convert them into diagonally dominant tensors for solving TCP.

Findings

Nekrasov Z tensors are contained within P-tensors.

A procedure to transform Nekrasov Z tensors into diagonally dominant tensors is proposed.

The class of Nekrasov Z tensors includes even ordered tensors with positive diagonals.

Abstract

It is worth knowing that a particular tensor class belongs to $P$-tensor which ensures the compactness to solve tensor complementarity problem (TCP). In this study, we propose a new class of tensor, Nekrasov $Z$ tensor, in the context of the tensor complementarity problem. We show that the class of $P$-tensor contains the class of even ordered Nekrasov $Z$ tensors with positive diagonal elements. In this context, we propose a procedure by which a Nekrasov $Z$ tensor can be transformed into a tensor which is diagonally dominant. Keywords: Diagonally dominant tensor, Nekrasov tensors, Nonsingular $H$ tensor, Nekrasov $Z$ tensor, $P$-tensors, Tensor complementarity problem