论文标题
LDU分解
LDU factorization
论文作者
论文摘要
矩阵的LU因素化是线性代数的基本算法之一。具有分布式内存的超级计算机的广泛使用需要对传统算法进行审查，这些算法基于计算机的共同内存。基质块递归算法是一类提供粗粒平行化的算法。在2010年获得了块递归LU分解算法。该算法称为Leu-Factorization。它像传统的lu-Algorithm一样，是为数字字段的矩阵而设计的。但是，它不能解决数值不稳定的问题。我们提出将LEU算法的概括为换向领域及其商领域的情况。该LDU分解算法将矩阵上的矩阵分解为三个矩阵的产物，其中矩阵L和U属于交换域，而加权截断的置换矩阵D的元素是与一对未成年人的乘积相反的元素。所有元素都是没有错误的计算，因此不会出现不稳定性问题。
LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a computer. Matrix block recursive algorithms are a class of algorithms that provide coarse-grained parallelization. The block recursive LU factorization algorithm was obtained in 2010. This algorithm is called LEU-factorization. It, like the traditional LU-algorithm, is designed for matrices over number fields. However, it does not solve the problem of numerical instability. We propose a generalization of the LEU algorithm to the case of a commutative domain and its field of quotients. This LDU factorization algorithm decomposes the matrix over the commutative domain into a product of three matrices, in which the matrices L and U belong to the commutative domain, and the elements of the weighted truncated permutation matrix D are the elements inverse to the product of some pair of minors. All elements are calculated without errors, so the problem of instability does not arise.
