Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators
Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators
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DOI：
10.1016/j.jcp.2016.06.011
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Benjamin Helmich-Paris;L. Visscher
中科院分区：
文献类型：
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作者：
Benjamin Helmich-Paris;L. Visscher
我们提出了一个强大的和非启发式的算法，找到所有的极值点的数值拉普拉斯变换的轨道能量转换器的误差分布函数。极值点搜索是求极小极大近似的两个关键步骤之一。如果预先制表的初始猜测是应该避免的，一个足够强大的算法的策略还没有讨论到目前为止。我们比较了我们的非启发式方法与括号和二分法算法，并证明了3倍少的功能评估时，需要将其应用到典型的非相对论和相对论量子化学系统。
We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.