标题： 截断汉克尔相关器方法 显示英文标题

标题： The Truncated Hankel Correlator Method

摘要： 我们引入了一种新方法，通过指数和来近似欧几里得关联函数。截断汉克尔关联器（THC）方法从可用的完整关联器数据构建一个汉克尔矩阵，并截断该汉克尔矩阵的特征谱。然后通过对得到的低秩近似应用普朗尼广义特征值方法进行处理。包括（块）普朗尼（以及等价地（块）兰佐斯）和广义特征值问题（GEVP）在内的大量代数关联器分析方法可以作为THC方法的次优特例再现出来。例如，可以将权重（如逆平方误差）包含在分析中，从而使结果具有接近最优的$\chi^2$-值。这使得THC方法在精神上非常类似于多态拟合的显式解，自然地包括了矩阵值关联器的情况。我们证明，一般来说，在指数数量上找到优于THC方法提供的近似是指数级困难的。此外，THC方法对噪声具有鲁棒性，并且需要相对较少的人工监督。最后，当应用于对称数据时，得到的能量谱在机器精度范围内保证是对称的。 显示英文摘要

摘要： We introduce a new method to approximate Euclidean correlation functions by exponential sums. The Truncated Hankel Correlator (THC) method builds a Hankel matrix from the full correlator data available and truncates the eigenspectrum of said Hankel matrix. It proceeds by applying the Prony generalised eigenvalue method to the thus obtained low-rank approximation. A large number of algebraic correlator analysis methods including (block) Prony (and equivalently (block) Lanczos) and the generalised eigenvalue problem (GEVP) can be reproduced as sub-optimal special cases of the THC method. Weights, for instance inverse square errors, can be included in the analysis, so that the result has a close to optimal $\chi^2$-value. This makes the THC method very similar in spirit to a closed form solution to multi-state fits, naturally including the case of matrix-valued correlators. We show that, in general, finding approximations better than those provided by the THC method is exponentially hard in the number of exponentials. Moreover, the THC method is robust against noise and requires comparably little human oversight. Finally, when applied to symmetric data, the obtained energy spectrum is guaranteed to be symmetric up to machine precision.