A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides
A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides
复制标题
具有多个右侧的复杂对称线性系统的无击穿分块COCG方法
DOI：
10.3390/sym11101302
复制
发表时间：
2019
期刊：
影响因子：
2.7
通讯作者：
Zhang Shao Liang
中科院分区：
文献类型：
--
作者：
Zhong Hong Xiu;Gu Xian Ming;Zhang Shao Liang
块共轭正交共轭梯度法（BCOCG）是求解多右端对称线性方程组的一种常用方法。然而，如果右侧排名不足，则总是会发生故障。本文基于正交性条件，提出了一种无故障的BCOCG算法，该算法引入了新的参数矩阵来处理秩亏问题。为了改善系数矩阵A的谱特性，提出了一种无故障BCOCG的预处理方案。给出了块共轭A-正交共轭残数法的相关算法。数值结果表明，当故障发生时，无故障算法比非故障算法产生更快的收敛速度。
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms.