A Fast GPU Algorithm for the Inverse of a Circulant Matrix
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.
Dongye Sun, Wen-Pei Sung and Ran Chen
Z. Y. Zheng and R. X. Zhang, "A Fast GPU Algorithm for the Inverse of a Circulant Matrix", Applied Mechanics and Materials, Vols. 121-126, pp. 3755-3759, 2012