Computation of a new error bound for tensor complementarity problem with P tensor

TL;DR

This paper introduces a new, sharper error bound for solving tensor complementarity problems involving P-tensors, improving upon previous bounds and applicable to even order positive diagonal tensors.

Contribution

It proposes a novel, more accurate error bound for TCP involving P-tensors, enhancing the theoretical understanding and solution accuracy.

Findings

The new error bound is sharper than existing bounds.

Established absolute and relative error bounds for even order positive diagonal tensors.

Applicable to a broad class of tensor complementarity problems.

Abstract

We propose a new error bound for the solution of tensor complementarity problem TCP$(q, \mathcal{A})$ given that $\mathcal{A}$ is a $P$-tensor and $q$ is a real vector. We show that the proposed error bound is sharper than the earlier version of error bound available in the literature. We establish absolute and relative error bound for TCP$(q, \mathcal{A})$ where $\mathcal{A}$ is an even order positive diagonal tensor. Keywords: Tensor complementarity problem, $P$-tensor, global error bound, positively homogeneous operator.