A NOTE ON THE LDL T DECOMPOSITION OF MATRICES FROM SADDLE-POINT PROBLEMS ∗
A NOTE ON THE LDL T DECOMPOSITION OF MATRICES FROM SADDLE-POINT PROBLEMS ∗
复制标题
关于鞍点问题矩阵的 LDL T 分解的注记 *
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Siam J. Matrix
中科院分区：
文献类型：
--
作者：
T. Miroslav;Siam J. Matrix
考虑稀疏线性系统 Kx = b，其中 K 是特殊结构的对称不定矩阵。这些系统经常出现，例如，来自偏微分方程问题的混合有限元离散化。已知 K 与对角线 D 和单位下三角 L 的 LDLT 分解对于 K 的自然排序来说是存在的，但生成的三角因子可能相当密集。另一方面，对于给定的置换矩阵 P ， P T KP 的 LDLT 因式分解可能不存在。本文介绍了一种基于初始填充最小化排序获得填充最小化排列的新方法。对于由混合有限元离散化产生的一个重要的矩阵子类，证明了置换矩阵的 LDL T 分解的存在性。实际问题的实验结果表明，与基于 Schur 补集的方法相比，可以节省大量计算量。
Sparse linear systems Kx = b are considered, where K is a specially structured sym- metric indefinite matrix. These systems arise frequently, e.g., from mixed finite element discretiza- tions of PDE problems. The LDLT factorization of K with diagonal D and unit lower triangular L is known to exist for natural ordering of K, but the resulting triangular factors can be rather dense. On the other hand, for a given permutation matrix P , the LDLT factorization of P T KP may not exist. In this paper a new way to obtain a fill-in minimizing permutation based on initial fill-in minimiz- ing ordering is introduced. For an important subclass of matrices arising from mixed and hybrid finite element discretizations, the existence of the LDL T factorization of the permuted matrix is proved. Experimental results on practical problems indicate that the amount of computational savings can be substantial when compared with the approach based on Schur complement.