Current results in fast algorithm computational complexity analysis, computer architecture design, and VLSI hardware advances with applications to digital signal processing

1991 ◽  
Vol 1 (1) ◽  
pp. 27-30
Author(s):  
Jim Schroeder
Keyword(s):  
Signal Processing ◽  
Computational Complexity ◽  
Digital Signal Processing ◽  
Computer Architecture ◽  
Fast Algorithm ◽  
Complexity Analysis ◽  
Digital Signal ◽  
Architecture Design ◽  
Analysis Computer

A Fast GPU Algorithm for the Inverse of a Circulant Matrix

2011 ◽  
Vol 121-126 ◽  
pp. 3755-3759
Author(s):  
Zuo Yong Zheng ◽  
Rui Xia Zhang
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
Toeplitz Matrix ◽  
Fast Algorithm ◽  
Digital Signal ◽  
Circulant Matrix ◽  
Frequency Space ◽  
Special Case

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.

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