ILU is a suite of parallel incomplete LU factorization algorithms featuring dual threshold (ILUT) and level-based (ILUK) variants. The implementation is based on a domain decomposition framework for achieving distributed parallelism.

ilu分解方法是一种迭代求解方法，顾名思义，它跟lu分解方法有一定的联系，lu分解方法是一种直接求解方法，当a为稀疏矩阵时，直接对a进行lu分解方法使得l和u丧失了矩阵a的稀疏性质，丧失了稀疏性质的矩阵的存储开销将增大，因此文献[1]中提出了ilu分解方法 ...

2003年5月1日 · In constructing an ILU(m) preconditioner (ILU of level m), we use the power of a Boolean matrix strategy (PBS) proposed by Mittal and Al-Kurdi (11 for determining the pattern of nonzero elements of the LU factors of the given matrix A. We also present an algorithm for computing the factors L and U.

1999年7月1日 · In this paper a multilevel-like ILU preconditioner is introduced. The ILU factorization generates its own ordering during the elimination process. Both ordering and dropping depend on the size...

2022年3月15日 · 之所以想到写这么一个东西是因为：我们数模课作业需要我们实现 ILU (0)算法，但是给的参考资料说的十分含糊，再加上网上能找到的中文参考资料很少很少，所以折腾了很久，查了很多资料才逐渐能够理解这个分解......既然好不容易弄懂了，而且也写了作业报告，就把它记录一下吧~（个人浅薄理解，如有错误还请指出） 之所以想到写这么一个东西是因为：我们数模课作业需要我们实现ILU (0)算法，但是给的参考资料说的十分含糊，再加上网上能找到的中文 …

使用共轭梯度法求解一个对称正定的稀疏矩阵，使用对称高斯-赛德尔和ilu(0)两种预调节器，记录每一步误差的范数 带预调节器的共轭梯度法的收敛曲线

We propose a parallel incomplete LU (ILU) preconditioned GMRES solver for those equations. A new subtree-based scheduling algorithm for ILU factorization and forward/backward substitution is...

2023年11月14日 · ilu 函数提供三种类型的不完全 LU 分解：零填充分解 (ILU(0))、Crout 版本 (ILUC)，以及具有阈值调降和主元消去的分解 (ILUTP)。 默认情况下，ilu 执行稀疏矩阵输入的零填充不完全 LU 分解。

In this paper a multilevel-like ILU preconditioner is introduced. The ILU factorization generates its own ordering during the elimination process. Both ordering and dropping depend on the size of the entries. The method can handle structured and unstructured problems.

NSILU consists of some numerical techniques such as simple modification of Schur complement, compression of ill-condition structure by permutation, nested simple ILU, and inner-outer iteration. We give detailed error analysis of NSILU and estimations of condition number of the preconditioned coefficient matrix, together with numerical comparisons.