Upper triangulation-based infinity norm bounds for the inverse of Nekrasov matrices with applications

The infinity norm bounds for the inverse of Nekrasov matrices play an important role in scientific computing. We in this paper propose a triangulation-based approach that can easily be implemented to seek sharper infinity norm bounds for the inverse of Nekrasov matrices. With the help of such sharper bounds, new error estimates for the linear complementarity problem of Nekrasov matrices are presented, and a new infinity norm estimate of the iterative matrix of parallel-in-time methods for an all-at-once system from Volterra partial integral-differential problems is given. Finally, these new bounds are compared with other state-of-the-art results so that the effectiveness of our proposed results is verified.