Electronic Research Archive (Mar 2023)
Partially doubly strictly diagonally dominant matrices with applications
Abstract
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.
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