Infinity Norm Bounds for the Inverse of $\textrm{SDD}_1$-Type Matrices with Applications

Abstract

A new subclass of H-matrices named $\textrm{SDD}_1$-type matrices is introduced. The relationships between $\textrm{SDD}_1$-type matrices and other subclasses of H-matrices are studied. Moreover, the infinite norm bounds for the inverse of $\textrm{SDD}_1$-type matrices are provided. As applications, error bounds of the linear complementarity problems (LCPs) for $\textrm{SDD}_1$-type matrices and strictly diagonally dominant ($\textrm{SDD}$) matrices strictly diagonally dominant (are also presented, which improve some existing bounds. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

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Funding

Guizhou Provincial Science and Technology Department(20191161)

Guizhou Provincial Youth Science and Technology Talents Growth Project(QJJ2023012)

RIGHTS & PERMISSIONS

Shanghai University