Conjugate Unscented Transform rules for uniform probability density functions
Conjugate Unscented Transform rules for uniform probability density functions
复制标题
均匀概率密度函数的共轭无味变换规则
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
T. Singh
中科院分区：
文献类型：
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作者：
Nagavenkat Adurthi;P. Singla;T. Singh
本文提出了几个新的求积规则来计算关于均匀概率密度函数的期望积分。在一维期望积分中，最广泛使用的数值方法是高斯-勒让德求积，因为它们对多项式是精确的。对于一般的N维积分，1维Gauss-Legendre求积的张量积导致点数的不期望的指数增长。本文提出的求积规则可以直接替代Gauss-Legendre求积规则，因为它们也被设计用于精确计算多项式的积分，但只使用一小部分点数。此外，它们也都具有正权重。
This paper presents a few novel quadrature rules to evaluate expectation integrals with respect to a uniform probability density function. In 1-dimensional expectation integrals the most widely used numerical method is the Gauss-Legendre quadratures as they are exact for polynomials. As for a generic N-dimensional integral, the tensor product of 1-dimensional Gauss-Legendre quadratures results in an undesirable exponential growth of the number of points. The cubature rules proposed in this paper can be used as a direct alternative to the Gauss-Legendre quadrature rules as they are also designed to exactly evaluate the integrals of polynomials but use only a small fraction of the number of points. In addition, they also have all positive weights.