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首页> 外文会议>International conference on large-scale scientific computing >Index Mapping between Tensor-Product Wavelet Bases of Different Number of Variables, and Computing Multivariate Orthogonal Discrete Wavelet Transforms on Graphics Processing Units
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Index Mapping between Tensor-Product Wavelet Bases of Different Number of Variables, and Computing Multivariate Orthogonal Discrete Wavelet Transforms on Graphics Processing Units

机译：不同数目的变量的张量积小波基之间的索引映射，以及在图形处理单元上计算多元正交离散小波变换

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摘要

An algorithm for computation of multivariate wavelet transforms on graphics processing units (GPUs) was proposed in [1]. This algorithm was based on the so-called isometric conversion between dimension and resolution (see [2] and the references therein) achieved by mapping the indices of orthonormal tensor-product wavelet bases of different number of variables and a tradeoff between the number of variables versus the resolution level, so that the resulting wavelet bases of different number of variables are with different resolution, but the overall dimension of the bases is the same.In P[1] we developed the algorithm only up to mapping of the indices of blocks of wavelet basis functions. This was sufficient to prove the consistency of the algorithm, but not enough for the mapping of the individual basis functions in the bases needed for a programming implementation of the algorithm. In the present paper we elaborate the full details of this 'book-keeping' construction by passing from block-matrix index mapping on to the detailed index mapping of the individual basis functions. We also consider some examples computed using the new detailed index mapping.
机译：在[1]中提出了一种在图形处理单元（GPU）上计算多元小波变换的算法。该算法基于尺寸和分辨率之间的所谓等距转换（请参见[2]及其参考），该等距转换是通过映射变量数不同的正交张量积小波基的索引以及变量数之间的权衡来实现的相对于分辨率级别，因此所得到的不同数量的变量的小波基具有不同的分辨率，但是基的整体维数是相同的。在P [1]中，我们开发的算法仅适用于块索引的映射小波基函数。这足以证明算法的一致性，但不足以映射算法的编程实现所需的基础中的各个基本函数。在本文中，我们通过从块矩阵索引映射到各个基本函数的详细索引映射，详细阐述了这种“簿记”构造的详细信息。我们还将考虑使用新的详细索引映射计算出的一些示例。

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