Band-restricted diagonally dominant matrices: Computational complexity and application

Norikazu Takahashi; Daiki Hirata; Shuji Jinbo; Hiroaki Yamamoto

doi:10.1016/j.jcss.2018.10.006

Band-restricted diagonally dominant matrices: Computational complexity and application

Norikazu Takahashi, Daiki Hirata, Shuji Jinbo, Hiroaki Yamamoto

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1016/j.jcss.2018.10.006
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

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10.1016/j.jcss.2018.10.006

Cite this

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title = "Band-restricted diagonally dominant matrices: Computational complexity and application",

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.",

keywords = "Band-restricted diagonally dominant matrix, Computational complexity, Convergence, Decision problem, Neural network",

author = "Norikazu Takahashi and Daiki Hirata and Shuji Jinbo and Hiroaki Yamamoto",

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AU - Hirata, Daiki

AU - Jinbo, Shuji

AU - Yamamoto, Hiroaki

N1 - Funding Information: The authors would like to thank anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. This work was supported by JSPS KAKENHI Grant Number JP15K00035 . Publisher Copyright: © 2018 Elsevier Inc.

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Band-restricted diagonally dominant matrices: Computational complexity and application

Abstract

Keywords

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