论文标题
一种用于评估具有特殊功能的快速矩阵矢量乘法的额外组件方法
An extra-components method for evaluating fast matrix-vector multiplication with special functions
论文作者
论文摘要
在计算积分或离散变换时，已使用快速算法将向量乘以矩阵的快速算法，其元素被指定为特殊（Chebyshev，legendre，legendre，laguerre等）函数的值。当前可用的快速算法比快速傅立叶变换的效率低几个数量级。为了提高效率，提出了一种方便的一般方法，用于计算某些类别问题的矩阵向量产品。可以使用基于现代微处理器的软件有效地实现了一系列在此方法下开发的快速简单结构算法。该方法具有$ O（n^2 \ log n）$的预紧要复杂性，执行复杂度为$ O（n \ log n）$。使用算法的计算实验结果表明，与矩阵矢量乘法的常规直接方法相比，这些过程可以减少几个数量级的计算时间。
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently available fast algorithms are several orders of magnitude less efficient than the fast Fourier transform. To achieve higher efficiency, a convenient general approach for calculating matrix-vector products for some class of problems is proposed. A series of fast simple-structure algorithms developed under this approach can be efficiently implemented with software based on modern microprocessors. The method has a pre-computation complexity of $O(N^2 \log N)$ and an execution complexity of $O(N \log N)$. The results of computational experiments with the algorithms show that these procedures can decrease the calculation time by several orders of magnitude compared with a conventional direct method of matrix-vector multiplication.
