论文标题
贪婪重建算法的分析
Analysis of a greedy reconstruction algorithm
论文作者
论文摘要
为一种贪婪的算法提供了一种新颖而详细的收敛分析，该算法先前是针对量子力学领域的运营商重建问题引入的。该算法基于重建过程的离线/在线分解以及ANSATZ，用于由一组先验选择的线性独立矩阵获得的未知操作员。提出的融合分析着重于线性差异系统控制的线性二次（优化）问题，并揭示了贪婪算法对系统的可观察性特性以及基础元素的ANSATZ的强烈依赖性。此外，该分析使我们能够为线性案例使用基本元素的精确（最佳）选择，并导致引入了一种新的，更强大的优化优化的贪婪重建算法。这种优化的方法还适用于非线性哈密顿重建问题，其效率通过数值实验证明。
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. The presented convergence analysis focuses on linear-quadratic (optimization) problems governed by linear differential systems and reveals the strong dependence of the performance of the greedy algorithm on the observability properties of the system and on the ansatz of the basis elements. Moreover, the analysis allows us to use a precise (and in some sense optimal) choice of basis elements for the linear case and led to the introduction of a new and more robust optimized greedy reconstruction algorithm. This optimized approach also applies to nonlinear Hamiltonian reconstruction problems, and its efficiency is demonstrated by numerical experiments.
