AI 中文总结
研究全组态相互作用基态问题的坐标下降法中压缩的作用，通过局部假设证明压缩迭代线性收敛，刻画收敛点，在特定假设下得出特征值误差阶数，数值结果支持分析。
AI 中文摘要
我们在全组态相互作用基态问题的无约束优化公式中研究压缩在坐标下降全组态相互作用（CDFCI）中的作用。在适当的局部假设下，证明了压缩迭代线性收敛到相关受限问题的解，还刻画了压缩算法的收敛点。在目标特征向量的额外指数衰减假设下，表明所得特征值误差为\(\tau^2\)阶，其中\(\tau\)为压缩阈值。数值结果支持该分析。
英文摘要
We study the effect of compression in Coordinate Descent Full Configuration Interaction (CDFCI) within an unconstrained optimization formulation of the full configuration interaction ground-state problem. Under suitable local assumptions, we prove that the compressed iteration converges linearly to the solution of an associated restricted problem. We also characterize the convergence point of the compressed algorithm. Under an additional exponential decay assumption on the target eigenvector, we show that the resulting eigenvalue error is of order $τ^2$, where $τ$ denotes the compression threshold. Numerical results support the analysis.
