鳞状循环因子矩阵逆矩阵的求法  

Methods for finding the inverses of scaled circulant factor matrices

作　　者：江兆林[1] 邓方安[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院

出　　处：《西安电子科技大学学报》2003年第3期415-420,共6页Journal of Xidian University

基　　金：国家自然科学基金资助项目(69972036)

摘　　要：利用插值法和矩阵的基本性质给出了复数域上的鳞状循环因子矩阵逆矩阵的一个计算公式,利用Schur.补给出了复数域上的具有鳞状循环因子矩阵块的分块矩阵的逆矩阵的一个算法,介绍了四元数除代数上的鳞状循环因子矩阵并给出了逆矩阵的一种求法.Scaled circulant factor matrices, as an important class g of special matrices, have a wide range of interesting applications in wavelet transform, signal processing, filter design, image processing image analysis, and so on. In this paper, a formula for calculating the inverse of a scaled circulant factor matrix over the complex field is given by using only the interpolation methods and basic properties of such matrices, and an algorithm for finding the inverse of partitioned matrix with scaled circulant factor matrix blocks over the complex field is presented by using the Schur complement. Finally, a scaled circulant factor matrix over the quaternion division algebra is introduced, and an algorithm for finding the inverse of such matrix is proposed.

关 键 词：鳞状循环因子矩阵 逆矩阵 分块矩阵 插值法 复数域 

分 类 号：O151.21[理学—数学]