Schur Complement-Based Determinant Bounds for SDD$_1$ Matrices

Abstract

The class of SDD$_1$ matrices is an important subclass of H-matrices. In this paper, we develop new two-sided determinant bounds for SDD$_1$ matrices by analyzing the structure of their Schur complements. Compared with existing bounds, our results are shown to be significantly tighter in most cases while remaining computable with similar effort.

Keywords

SDD$_1$ matrices / Determinant / Schur complement / Diagonally dominant degree / 15A15

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