Band-restricted diagonally dominant matrices: Computational complexity and application

Norikazu Takahashi, Daiki Hirata, Shuji Jinbo, Hiroaki Yamamoto

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)100-111
Number of pages12
JournalJournal of Computer and System Sciences
Volume101
DOIs
Publication statusPublished - 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

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