An Infinity Norm Upper Bound for the Inverse of $\hbox {SDD}_1$ Matrices and the Application in Linear Complementarity Problems

Abstract

The class of SDD$_1$ matrices is an important subclass of H-matrices. The strictly diagonally dominant (SDD) matrices, the doubly strictly diagonally dominant (DSDD) matrices, and the Dashnic Zusmanovich type (DZT) matrices are included in SDD$_1$ matrices. This paper presents an infinity norm upper bound for the inverse of SDD$_1$ matrices using the definition of the matrix norm. We prove that it is sharper than the well-known Varah’s bound for SDD matrices, and it generally performs better than the existing bounds for SDD$_1$, DSDD, and DZT matrices. As an application, an error bound for the linear complementarity problems (LCPs) of B$_1$-matrices is given.

Keywords

$_1$ matrix')">SDD$_1$ matrix / Infinity norm / Linear complementarity problems (LCPs) / 15A45 / 15A48 / 65F05

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