On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
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DOI：
10.1140/epja/s10050-020-00205-w
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发表时间：
2020-04
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影响因子：
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通讯作者：
M. Fischer;B. Kostrzewa;J. Ostmeyer;K. Ottnad;M. Ueding;C. Urbach
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作者：
M. Fischer;B. Kostrzewa;J. Ostmeyer;K. Ottnad;M. Ueding;C. Urbach
讨论了晶格QCD模拟中确定能级的各种方法之间的关系：广义特征值法、Prony法、广义函数束法和Gardner法。前三种方法都可以理解为广义特征值问题的特殊情况。我们解析地表明，在所有三种方法中，由于未解析态的导致的能量的主要修正都呈指数型渐近衰减。用综合数据表明，这些修正在实践中也符合预期。我们提出了一种将广义特征值与proony方法相结合的新方法，表示为GEVM/PGEVM，该方法有助于增加能隙。我们用点阵QCD的例子来说明它的用法和性能。另一方面，Gardner方法被发现不太适用于实际的噪声数据。
We discuss the relation of a variety of different methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony, the generalised pencil of function and the Gardner methods. All three former methods can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energyin all three methods due to unresolved states decay asymptotically exponentially like. Using synthetic data we show that these corrections behave as expected also in practice. We propose a novel combination of the generalised eigenvalue and the Prony method, denoted as GEVM/PGEVM, which helps to increase the energy gap. We illustrate its usage and performance using lattice QCD examples. The Gardner method on the other hand is found less applicable to realistic noisy data.