稀疏线性方程组不完全分解预条件方法

稀疏线性方程组的高效求解在科学计算与工程应用中起着十分重要的作用。本文系统介绍一般稀疏线性方程组和块三对角线性方程组的不完全预条件构造技术，同时介绍我们提出的多行双门槛不完全分解预条件子MRILUT和局部块不完全分解预条件子LBF2（l）构造方法，并将它们应用于二维三温能量方程组的离散求解与二维Laplace微分方程的离
离散求解中，取得了满意的结果。

An Incomplete Decomposition Preconditioning Method for Sparse Linear Equations

The high-performance solution to sparse linear equations is very important in science and engineering applications. In this paper, we introduce an incomplete decomposition preconditioning method for general sparse matrices and block tridiagonal matrices. We introduce simultaneously two preconditioning methods, the multiple row incomplete decomposition(MRILUT) and the local block factorization(LBF2(l)). These methods have been applied to the discrete solution of two-dimensional three-temperature energy equations and two-dimensional Laplace equations, and the results are satisfactory.