论文标题
自洽场迭代的最佳收敛速率，用于解决依赖特征向量的非线性特征值问题
Optimal Convergence Rate of Self-Consistent Field Iteration for Solving Eigenvector-dependent Nonlinear Eigenvalue Problems
论文作者
论文摘要
我们提出了针对自洽场（SCF）迭代的全面融合分析，以解决特征向量依赖性（NEPV）的一类非线性特征值问题。使用切线角矩阵作为近似误差的中间度量，我们为两个基本量的新公式建立了新的公式，以最佳地表征普通SCF的局部收敛：局部收缩因子和局部平均收缩因子。与先前确定的结果相比，新的收敛速率估计值在收敛速度上提供了很大的界限。作为一个应用程序，我们将收敛分析扩展到流行的SCF变体-SCF SCF。在电子结构计算中求解Kohn-Sham方程以及在Bose-Einstein Conensation建模中，在电子结构计算中求解Kohn-Sham方程而产生的NEPV的有效性是在数值上证明的。
We present a comprehensive convergence analysis for Self-Consistent Field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector-dependency (NEPv). Using a tangent-angle matrix as an intermediate measure for approximation error, we establish new formulas for two fundamental quantities that optimally characterize the local convergence of the plain SCF: the local contraction factor and the local 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 NEPv arising from solving the Kohn-Sham equation in electronic structure calculation and the Gross-Pitaevskii equation in the modeling of Bose-Einstein condensation.
