Sharp Convergence Estimates for the Preconditioned Steepest Descent Method for Hermitian Eigenvalue Problems
Sharp Convergence Estimates for the Preconditioned Steepest Descent Method for Hermitian Eigenvalue Problems
复制标题
Hermitian 特征值问题的预处理最速下降法的锐收敛估计
DOI：
10.1137/040620643
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
E. Ovtchinnikov
中科院分区：
文献类型：
--
作者：
E. Ovtchinnikov
研究了计算厄米算子最小特征值的预条件最陡下降法的收敛性估计。对现有的估计进行审查，并引入在某些方面改进已知估计的新估计。除了对一次迭代后的误差减少的估计外，我们还考虑了所谓的渐近收敛因子的估计，该因子被定义为每次迭代的平均误差减少的上限。本文着重于尖锐的估计，即那些不使用附加信息就无法改进的估计。
The paper is concerned with convergence estimates for the preconditioned steepest descent method for the computation of the smallest eigenvalue of a Hermitian operator. Available estimates are reviewed and new estimates are introduced that improve on the known ones in certain respects. In addition to the estimates for the error reduction after one iteration, we consider estimates for the so-called asymptotic convergence factor defined as the upper limit of the average error reduction per iteration. The paper focuses on sharp estimates, i.e., those that cannot be improved without using additional information.