论文标题
关于广义特征值法及其与Prony和广义铅笔的关系
On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
论文作者
论文摘要
我们讨论了确定晶格QCD模拟中能量水平的三种方法的关系：广义特征值，prony和广义铅笔的功能方法。这三个都可以理解为广义特征值问题的特殊情况。我们分析地表明，由于未解决的状态衰减在所有三种方法中，对能量$ e_l $的领先校正在毫无疑问上呈指数级，就像$ \ exp（ - （e_ {n} -e_l）t）$。使用合成数据，我们表明这些校正在实践中也如预期的那样行事。我们提出了广义特征值和prony方法的新颖组合，称为GEVM/PGEVM，这有助于增加能量差距$ e_ {n} -e_l $。我们使用晶格QCD示例说明了其使用和性能。
We discuss the relation of three methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony and the generalised pencil of function methods. All three can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energy $E_l$ in all three methods due to unresolved states decay asymptotically exponentially like $\exp(-(E_{n}-E_l)t)$. 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 $E_{n}-E_l$. We illustrate its usage and performance using lattice QCD examples.
