Before revision:  In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the corresponding TL-OS preconditioned algorithmic and theoretical frameworks  .
After revision:  In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the corresponding TL-OS preconditioned algorithmic and theoretical frameworks of the corresponding TL-OS methods .