Error Bound for the Linear Complementarity Problem using Plus Function

TL;DR

This paper derives error bounds for the linear complementarity problem with P-matrices using the plus function, introducing a new fundamental quantity to improve understanding of solution stability.

Contribution

It introduces a new fundamental quantity related to P-matrices and uses it to establish error bounds for the linear complementarity problem, advancing theoretical understanding.

Findings

Established error bounds for P-matrix LCPs using the plus function

Introduced a new fundamental quantity associated with P-matrices

Derived bounds for this quantity, enhancing solution analysis

Abstract

In this article we establish error bound for linear complementarity problem with $P$-matrix using plus function. We introduce a fundamental quantity associated with a $P$-matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the $P$-type. We also obtain (upper and lower) bounds for the quantity introduced. Keywords: Linear complementarity problem, plus function, error bound, relative error bound.