Abstract
As a generalization of diagonally dominant matrices, we introduce a new class of square matrices called band-restricted diagonally dominant (BRDD) matrices. We prove that the problem of determining whether a given square matrix of order n is permutation-similar to some BRDD matrix is in P when the lower bandwidth l is 0 and the upper bandwidth u is n−1, while the problem is NP complete when l=0 and u belongs to some set of integers containing 1. We next show that a special class of BRDD matrices plays an important role in the convergence analysis of discrete-time recurrent neural networks.
Original language | English |
---|---|
Pages (from-to) | 100-111 |
Number of pages | 12 |
Journal | Journal of Computer and System Sciences |
Volume | 101 |
DOIs | |
Publication status | Published - May 2019 |
Keywords
- Band-restricted diagonally dominant matrix
- Computational complexity
- Convergence
- Decision problem
- Neural network
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics