关于修正的逐成分构造
On a projection-corrected component-by-component construction
AI总结：
本文研究一种修正的逐成分构造算法，强制各成分互异，避免投影问题，推导了新的误差界。
摘要：
逐成分构造是寻找良好格点规则或多项式格点规则的标准方法。几位作者报告称在数值实验中生成向量有时会有重复成分。我们研究了一种经典逐成分算法的变体，用于构造格点或多项式格点集，其中各成分被强制不同。这避免了所有取样点落在主对角线上的投影问题。由于先前关于最坏情况误差的结果不适用于此修改算法，我们在此证明了此类误差界。我们还讨论了进一步限制成分选择的条件。
英文摘要：
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes has repeated components. We study a variation of the classical component-by-component algorithm for the construction of lattice or polynomial lattice point sets where the components are forced to differ from each other. This avoids the problem of having projections where all quadrature points lie on the main diagonal. Since the previous results on the worst-case error do not apply to this modified algorithm, we prove such an error bound here. We also discuss further restrictions on the choice of components in the component-by-component algorithm.
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