Stability of the block cyclic reduction
Stability of the block cyclic reduction
复制标题
块循环约简的稳定性
DOI：
10.1016/0024-3795(95)00392-4
复制
发表时间：
1996
影响因子：
1.1
通讯作者：
V. Pavlov
中科院分区：
文献类型：
--
作者：
P. Yalamov;V. Pavlov
研究了块体三对角线体系无反取代的块体循环约简的正向稳定性。基本假设是系统的矩阵是块列对角占优的。然后表明，对于非严格对角占优矩阵，前向误差为O(Cnn2log2nκϱ0)，对于严格对角占优矩阵，前向误差为O(Cng(s) log2nκϱ0)，其中n是矩阵的块大小，n是每个块的大小，g(s)是度量对角占优的函数，κ是一个条件数，ϱ0is是机器舍入单位。最后给出了一些数值证据。
The forward stability of the block cyclic reduction without back substitution for block tridiagonal systems is studied. The basic assumption is that the matrix of the system is block column diagonally dominant. Then it is shown that for nonstrictly diagonally dominant matrices the forward error is O(Cnn2log2nκϱ0), and for strictly diagonally dominant matrices it is O(Cng(s) log2nκϱ0), where n is the block size of the matrix, N is the size of each block, g(s) is a function which measures the diagonal dominance, κ is a condition number, and ϱ0is the machine roundoff unit. At the end some numerical evidence is presented.