This article presents enhancement strategies for the Hermitian and skew‐Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In particular, steepest descent with early stopping can generate a rough estimate of the optimal upper bound. This is better than an arbitrary choice since the latter often causes stability problems or slow convergence. In addition, delayed gradient methods are considered as inner solvers for the splitting method. Experiments verify the effectiveness of the proposed estimation strategies and show that delayed gradient methods are competitive with conjugate gradient in low precision.

中文翻译：

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使用梯度迭代的Hermitian和Skew-Hermitian分裂方法中的参数估计

本文介绍了基于梯度迭代的Hermitian和skew-Hermitian分裂方法的增强策略。频谱特性被用于参数估计，通常会导致更好的收敛性。特别是，在提前停止的情况下，最陡峭的下降会产生最佳上限的粗略估计。这比任意选择要好，因为后者经常会导致稳定性问题或收敛缓慢。另外，延迟梯度方法被认为是分裂方法的内部求解器。实验验证了所提估计策略的有效性，并表明延迟梯度法与共轭梯度法相比具有较低的精度。