In this work, a class of inexact block SSOR-like preconditioners are proposed for the non-Hermitian positive definite linear system whose coefficient matrix is of a blockwise form. The novel preconditioners are based on the SSOR-like iteration method proposed by Bai (Numer. Linear Algebra Appl. 23, 37-60, 2016), but each of the diagonal blocks in the SSOR-like method is replaced by an approximation matrix which is easier to deal with. The estimated bounds for eigenvalues of the new preconditioned matrix, as well as the convergence property about the corresponding iteration method, are discussed. Finally, numerical experiments arise from the discretization of two-dimensional fractional diffusion equation and two-dimensional linear integro-differential equation are presented to confirm the theoretical analyses and illustrate the efficiency of the new preconditioners.

在这项工作中，针对其系数矩阵为块形式的非Hermitian正定线性系统，提出了一类不精确的类似于SSOR的预处理器。新颖的预处理器基于Bai（Numer。Linear Algebra Appl。23，37-60，2016）提出的类SSOR迭代方法，但是类SSOR方法中的每个对角线块都被近似矩阵代替。更容易处理。讨论了新的预处理矩阵特征值的估计边界，以及有关相应迭代方法的收敛性。最后，