Cross correlation functions Cnm(E) via Lanczos algorithms without diagonalization
Cross correlation functions Cnm(E) via Lanczos algorithms without diagonalization
复制标题
通过 Lanczos 算法（无需对角化）的互相关函数 Cnm(E)
DOI：
10.1063/1.1515767
复制
发表时间：
2002
影响因子：
4.4
通讯作者：
S. Holmgren
中科院分区：
文献类型：
--
作者：
H. O. Karlsson;S. Holmgren
展示了如何修改基于 Lanczos 算法的拟最小残差算法 (QMR)，以通过递归更新少量标量来计算互相关函数 Cnm(E)=<Ψn|(E−H)−1|Ψm>，而无需任何对角化。只需要存储三个 Lanczos 向量。几个左侧向量<Ψn|可以同时考虑多个班次E。新方法被称为准最小递归残差生成方法（QM-RRGM），并应用于共线 H+H2 问题以说明其收敛行为。还讨论了 Lanczos 算法的两种不同公式的属性，即通常的三项递归和耦合的两项递归。 QM-RRGM 表现出平滑的收敛行为，并且表明 QMR 算法中使用的停止准则也可以用于计算相关函数。
It is shown how the quasiminimal residual algorithm (QMR), based on the Lanczos algorithm, can be modified to compute cross-correlation functions Cnm(E)=〈Ψn|(E−H)−1|Ψm〉 without any diagonalization by recursively updating a small number of scalars. Only three Lanczos vectors need to be stored. Several left-hand side vectors 〈Ψn| and multiple shifts E can be considered simultaneously. The new method is termed the quasiminimal recursive residue generation method (QM-RRGM) and is applied to the collinear H+H2 problem to illustrate its convergence behavior. The properties of two different formulations of the Lanczos algorithm, the usual three-term and a coupled two-term recursion, are also discussed. The QM-RRGM exhibits smooth convergence behavior, and it is shown that the stopping criteria used in the QMR algorithm can also be used for computing correlation functions.