Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper

Detectable MeV neutrinos from black hole neutrino-dominated accretion flows

Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes (BHs) have been theorized as the central engine of relativistic jets launched in massive star core collapse events or compact star mergers. In this work, we calculate the electron neutrino/anti-neutrino spectra of NDAFs by fully taking into account the general relativistic effects, and investigate the effects of viewing angle, BH spin, and mass accretion rate on the results. We show that even though a typical NDAF has a neutrino luminosity lower than that of a typical supernova (SN), it can reach $10^{50}-10^{51}~{\rm erg~s^{-1}}$ peaking at $\sim 10$ MeV, making them potentially detectable with the upcoming sensitive MeV neutrino detectors if they are close enough to Earth. Based on the observed GRB event rate in the local universe and requiring that at least 3 neutrinos are detected to claim a detection, we estimate a detection rate up to $\sim$ (0.10-0.25) per century for GRB-related NDAFs by the Hyper-Kamiokande (Hyper-K) detector if one neglects neutrino oscillation. If one assumes that all Type Ib/c SNe have an engine-driven NDAF, the Hyper-K detection rate would be $\sim$ (1-3) per century. By considering neutrino oscillations, the detection rate may decrease by a factor of 2-3. Detecting one such event would establish the observational evidence of NDAFs in the universe.Comment: 7 pages, 2 figures, 2 tables, accepted for publication in PR