Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations
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摘要: 非Hermite线性方程组在科学和工程计算中有着重要的理论研究意义和使用价值,因此如何高效求解该类线性方程组,一直是研究者所探索的方向.通过提出一种预处理方法,对非Hermite线性方程组和具有多个右端项的复线性方程组求解的若干迭代算法进行预处理,旨在提高原算法的收敛速度.最后通过数值试验表明,所提出的若干预处理迭代算法与原算法相比较,预处理算法迭代次数大大降低,且收敛速度明显优于原算法.除此之外,广义共轭A-正交残量平方法(GCORS2)的预处理算法与其他算法相比,具有良好的收敛性行为和较好的稳定性.
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关键词:
- 非Hermite线性方程组 /
- 广义共轭A-正交残量平方法 /
- 预处理方法
Abstract: Non-Hermitian linear equations have extensive application in scientific and engineering calculations and are expected to be solved with high efficiency. To accelerate the convergence rate of original algorithms, a preconditioning technique was developed and applied to some iterative methods chosen to solve the nonHermitian linear equations and complex linear systems with multiple righthand sides. Several numerical experiments show that the preconditioned iterative methods are superior to the original methods in terms of both the convergence rate and the number of iterations. In addition, the preconditioned generalized conjugate A-orthogonal residual squared method (GCORS2) has better convergent behavior and stability than other preconditioned methods. -
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