AI 中文总结
针对厄米特特征值问题提出JD-V方法，基于新校正方程，内部迭代在处理高度聚集特征值时更高效，开发厚重启算法计算多个特征对，数值实验表明其在整体效率上优于标准JD方法。
AI 中文摘要
本文提出了一种用于厄米特特征值问题的新型雅可比 - 戴维森（JD）型方法，即JD-V。它基于新设计的校正方程，其解在子空间扩展方面几乎与标准校正方程一样有效。对求解这些方程的MINRES进行严格收敛分析表明，当关注高度聚集的特征值时，JD-V的内部迭代比标准JD方法更高效。还开发了带收缩和净化的厚重启JD-V算法来计算大型厄米特矩阵的多个特征对。数值实验证实了理论结果，并表明JD-V在整体效率上比标准JD具有显著优势。
英文摘要
A novel variant of the Jacobi-Davidson (JD) type method for Hermitian eigenvalue problems, designated as JD-V, is proposed based on a newly designed correction equation, whose solution is shown to be nearly as effective as that of the standard correction equation for subspace expansion. Rigorous convergence analysis of MINRES for solving these equations reveals that the inner iterations of JD-V are significantly more efficient than those of the standard JD method when highly clustered eigenvalues are of interest. A thick-restart JD-V algorithm with deflation and purgation is developed to compute several eigenpairs of a a large-scale Hermitian matrix. Numerical experiments confirm the theoretical results and demonstrate the considerable superiority of JD-V over standard JD in overall efficiency.
Comments20 pages, 4 figures
