TY - JOUR
T1 - Band-restricted diagonally dominant matrices
T2 - Computational complexity and application
AU - Takahashi, Norikazu
AU - Hirata, Daiki
AU - Jimbo, 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.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2019/5
Y1 - 2019/5
N2 - 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.
AB - 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.
KW - Band-restricted diagonally dominant matrix
KW - Computational complexity
KW - Convergence
KW - Decision problem
KW - Neural network
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U2 - 10.1016/j.jcss.2018.10.006
DO - 10.1016/j.jcss.2018.10.006
M3 - Article
AN - SCOPUS:85057412888
VL - 101
SP - 100
EP - 111
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
SN - 0022-0000
ER -