Electronic Research Archive (Mar 2023)

Partially doubly strictly diagonally dominant matrices with applications

  • Yi Liu,
  • Lei Gao ,
  • Tianxu Zhao

DOI
https://doi.org/10.3934/era.2023151
Journal volume & issue
Vol. 31, no. 5
pp. 2994 – 3013

Abstract

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A new class of matrices called partially doubly strictly diagonally dominant (for shortly, PDSDD) matrices is introduced and proved to be a subclass of nonsingular $ H $-matrices, which generalizes doubly strictly diagonally dominant matrices. As applications, a new eigenvalue localization set for matrices is given, and an upper bound for the infinity norm bound of the inverse of PDSDD matrices is presented. Based on this bound, a new pseudospectra localization for matrices is derived and a lower bound for distance to instability is obtained.

Keywords