Band-restricted diagonally dominant matrices: Computational complexity and application

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.