The “ Combining Coefficient ” for Anisotropic Sparse Grids
The “ Combining Coefficient ” for Anisotropic Sparse Grids
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各向异性稀疏网格的“组合系数”
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Burkardt
中科院分区：
文献类型：
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作者：
J. Burkardt
各向异性稀疏网格是各向同性稀疏网格的自然扩展，适用于数据的行为随特定空间维度而变化的情况。适当配置的各向异性稀疏网格可以达到与各向同性稀疏网格相当的精度，同时与乘积规则相比，各向异性稀疏网格提供的函数计算次数进一步减少。将各向同性稀疏网格算法修改为各向异性稀疏网格算法，需要改变与分量积规则相关的选择准则和组合系数。本文将讨论这些更改及其在特定计算机代码中的实现。
The anisotropic sparse grid is a natural extension of the isotropic sparse grid, adapted for situations in which the behavior of the data varies with respect to particular spatial dimensions. An appropriately configured anisotropic sparse grid can achieve accuracy comparable to that of an isotropic sparse grid, while further compounding the reduction in the number of function evaluations that an isotropic sparse grid offers compared to a product rule. To modify an isotropic sparse grid algorithm into an anisotropic one requires changes to the selection criterion and the combining coefficients used in connection with the component product rules. This article discusses these changes and their implementation in a particular computer code.