For the large and sparse linear systems, we utilize the efficient splittings of the system matrix and introduce an intermediate variable. The main contribution of this paper is that the adaptive parameter based matrix splitting iteration method is constructed from the view of numerical optimization and hybrid procedure to solve the derived equation instead. The novel method adopts the prediction and correction two-step iteration and the global convergence results are established under some suitable conditions. Compared with some well-known methods, numerical experiments show the efficiency and effectiveness of the new proposal with application to the three-dimensional convection-diffusion equation and the image restoration problems.

对于大型稀疏线性系统，我们利用系统矩阵的有效分裂并引入中间变量。本文的主要贡献是从数值优化和混合过程的角度构建了基于自适应参数的矩阵分裂迭代方法来代替求解导出的方程。新方法采用预测和修正两步迭代，在一些合适的条件下建立了全局收敛结果。与一些著名的方法相比，数值实验证明了新提议在三维对流-扩散方程和图像恢复问题中的有效性和有效性。