一种特殊稀疏矩阵的LU分解加速技巧

A New Technique for Accelerating the LU Factorization of a Special Class of Sparse Matrix

随着待求解问题的维数的增加以及网格的加密，在数值计算过程中产生的稀疏线性方程组的求解便成了计算过程中最消耗计算资源的模块。在本文中我们根据问题本身所产生的矩阵的特殊结构，设计了一种精巧的 PR （Permutation and Reduction）置换约减算法，可以有效地减少矩阵的维数，减少矩阵分解过程中的填充，加快了分解的速度。

With the increase of the dimension of the computational problems, solving the sparse linear equations is the most time-consuming. In this paper, a new method is presented for a class of matrices with special sparse structure. Based on this, we propose a new method called PR（Permutation and Reduction） method. After performing the permutation and reduction, the original matrix is reduced to a smaller matrix which has the same sparse structure as the corresponding submatrix of the original matrix. The numerical experiments also show the efifciency of the new method.