Sharp Estimation of Convergence Rate for Self-Consistent Field Iteration to Solve Eigenvector-Dependent Nonlinear Eigenvalue Problems
Sharp Estimation of Convergence Rate for Self-Consistent Field Iteration to Solve Eigenvector-Dependent Nonlinear Eigenvalue Problems
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DOI：
10.1137/20m136606x
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发表时间：
2022-02
期刊：
影响因子：
--
通讯作者：
Z. Bai;Ren-Cang Li;Ding Lu
中科院分区：
文献类型：
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作者：
Z. Bai;Ren-Cang Li;Ding Lu
对求解一类特征向量相关的非线性特征值问题的自洽场迭代法进行了全面的收敛性分析。使用的切角矩阵作为一个中间措施的近似误差，我们建立了新的公式的两个基本量的局部收敛行为的平原SCF：局部收缩因子和局部渐近平均收缩因子。与以前建立的结果相比，新的收敛速度估计提供了更清晰的边界上的收敛速度。作为一个应用，我们将收敛性分析扩展到一个流行的SCF变体-水平移位SCF。数值计算表明收敛速度估计的有效性NEPvs所产生的解决Kohn-Sham方程的电子结构计算和Gross-Pitaevskii方程的玻色-爱因斯坦凝聚的建模。
We present a comprehensive convergence analysis for the self-consistent field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector dependency (NEPvs). Using the tangent-angle matrix as an intermediate measure for approximation error, we establish new formulas for two fundamental quantities that characterize the local convergence behavior of the plain SCF: the local contraction factor and the local asymptotic average contraction factor. In comparison with previously established results, new convergence rate estimates provide much sharper bounds on the convergence speed. As an application, we extend the convergence analysis to a popular SCF variant---the level-shifted SCF. The effectiveness of the convergence rate estimates is demonstrated numerically for NEPvs arising from solving the Kohn--Sham equation in electronic structure calculation and the Gross--Pitaevskii equation for modeling of the Bose--Einstein condensation.