一种新的快速反循环分块Jacket变换  

Novel Fast Anti-circulant Block Jacket Transform

作　　者：刘桂波[1] 罗大庸[1] 谢才浪 郭迎[1] 李门浩 

机构地区：[1]中南大学信息科学与工程学院,长沙410083 [2]全北国立大学信息与通信工程系

出　　处：《小型微型计算机系统》2016年第2期389-394,共6页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61379153;61272495)资助;新世纪优秀人才支持计划项目(NCET-11-0510)资助;韩国基础研究项目(2010-0020942;2012-002521)资助

摘　　要：受反循环矩阵和Jacket变换的启发,给出反循环分块Jacket变换对应的矩阵结构,进而获得了其任意阶的构造方法,丰富了Jacket变换的内容.随后基于克罗内克积及高阶反循环分块Jacket矩阵对应的置换矩阵,提出了该Jacket变换的前后向矩阵的一种递归形式的快速构造与分解算法.相比直接计算方法,该快速算法拥有更低的计算复杂度.而且本文提出的构造方法及快速算法也可以应用到其它具有类似结构的其它反循环分块Jacket变换中.Motivated by both anti-circulant matrix and Jacket transform, this paper firstly gave the matrix structure of the anti-circulant block Jacket transform, obtained construction method tailored to any size, and extended the Jacket family. Subsequently a fast construc- ting and decomposing algorithms with a recursive form for the forward and backward matrices corresponding to the anti-circulant block Jacket transform were successively derived based on the Kronecker product and permutation matrices adapting to the mentioned Jacket transform. Compared to the direct computation algorithm, the fast algorithm possesses a much lower computation complexity. Further- more the proposed construction method and fast algorithm can be also applied to other anti-circulant block Jacket transforms with simi- lar structures.

关 键 词：Jacket变换 反循环矩阵 反循环分块Jacket变换 克罗内克积 快速算法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]