高维数值积分的Sloan点阵法的最佳点阵

The best lattice points of Sloan lattice rules on multidimensional numerical integration

给出了一类高维数值积分的求积点阵,证明它是运用Sloan点阵法理论上所能达到的最佳情形.同时指出Коробов和Бахалов的极值系数方法在一定条件下可以改进到数论方法理论上的阶,并且理论与数值试验的结果是一致的.

The author gives a lattice rule in multi-dimensional numerical integration, and demonstrates that it is the best case in theoretical methods to make use of Sloan lattice rules. Meanwhile, he shows that optimal parameter method can be improved to its ideal order in theorem number on the suitable conditions, and the theory is confirmed by numerical results.