A fast GPU algorithm for the inverse of a circulant matrix

机译：一种快速GPU算法循环矩阵的逆

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Circulant matrix is a special case of Toeplitz matrix,which is widely used in many domains of specialization,especially in image and digital signal processing.Calculating the inverse of this category of matrices consists of the following three steps:(1) transform the first row vector to frequency space by using DFT; (2) calculate the inverse of each amplitude in the spectrum; (3) apply IDFT to the adjusted spectrum and reconstruct the inverse of the original circulant matrix.This paper implements such a fast algorithm on the GPU,which is proved around five to ten times faster than is executed on the CPU.

机译：循环矩阵是Toeplitz矩阵的特殊情况，它广泛用于专业的许多领域，尤其是在图像和数字信号处理中。乘积此类别的矩阵的倒数由以下三个步骤组成：（1）转换第一行矢量通过DFT向频率空间; （2）计算频谱中每个幅度的倒数; （3）将IDFT应用于调整后的频谱并重建原始循环矩阵的逆。此纸在GPU上实现了这种快速算法，其在CPU上执行的速度快约五到十倍。

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《International conference on frontiers of manufacturing and design science》|2012年||共5页
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Zuoyong Zheng; Ruixia Zhang;
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中图分类机械制造工艺;
关键词
circulant matrix; Discrete Fourier Transform; GPU; OpenGL; GLSL; fragment shader;

机译：循环矩阵;离散傅里叶变换;gpu;OpenGL;GLSL;片段着色器;

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专利

1. A NEW ALGORITHM FOR COMPUTING THE INVERSE AND GENERALIZED INVERSE OF THE SCALED FACTOR CIRCULANT MATRIX [J] . Zhaolin Jiang, Zongben Xu Journal of Computational Mathematics . 2008,第1期

机译：计算尺度因子循环矩阵的逆和广义逆的新算法
2. Fast Algorithms for Solving FLSR-Factor Block Circulant Linear Systems and Inverse Problem ofAX=b [J] . ZhaolinJiang Abstract and applied analysis . 2014,第2期

机译：解FLSR-因子块循环线性系统的快速算法和AX = b的反问题
3. Fast algorithms for solving the inverse problem of AX = b in the class of the ULS r-circulant (retrocirculant) matrices [J] . Zhiping Tian International journal of algebra . 2011,第9a12期

机译：在ULS r循环（逆循环）矩阵类别中解决AX = b逆问题的快速算法
4. A fast GPU algorithm for the inverse of a circulant matrix [C] . Zuoyong Zheng, Ruixia Zhang International conference on frontiers of manufacturing and design science . 2012

机译：循环矩阵逆的快速GPU算法
5. Fast algorithms for sparse matrix inverse computations. [D] . Li, Song. 2009

机译：稀疏矩阵逆计算的快速算法。
6. SIML: A Fast SIMD Algorithm for Calculating LINGO Chemical Similarities on GPUs and CPUs [O] . Imran S. Haque, Vijay S. Pande, W. Patrick Walters -1

机译：sImL：一种快速sImD算法计算在GpU和CpU LINGO化学相似性
7. Fast Algorithms for Solving FLSR-Factor Block Circulant Linear Systems and Inverse Problem ofAX=b [O] . Zhaolin Jiang 2014

机译：用于求解FLSR系数块循环线性系统的快速算法及逆问题= B.

A fast GPU algorithm for the inverse of a circulant matrix

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