### 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 |
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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

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## Cite this

Takahashi, N., Hirata, D., Jinbo, S., & Yamamoto, H. (2019). Band-restricted diagonally dominant matrices: Computational complexity and application.

*Journal of Computer and System Sciences*,*101*, 100-111. https://doi.org/10.1016/j.jcss.2018.10.006