块结构r-循环矩阵的性质及其算法研究  

Properties of r-Circulant Matrices of Block Structure and Their Algorithm Research

作　　者：史雨梅 秦梅[1] SHI Yumei;QIN Mei(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2018年第4期312-316,共5页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11601332);沪江基金资助项目(B14005)

摘　　要：提出了一种新的块循环矩阵,称之为块首尾差r-循环矩阵(简记为bFLDCM_r)。首先,验证了其线性运算结果和矩阵乘积仍是bFLDCM_r;其次,给出了bFLDCM_r的判别法和非奇异性判定的充要条件,并讨论了bFLDCM_r的对角化;最后,利用Sherman-Morrison-Woodbury公式,给出了三对角块r-循环线性系统求解的直接算法。A new type of matrices which is called the first and the last difference r-block circulant matrix(bFLDCMr)was presented.The linear operation and the matrix product were verified to bFLDCMr.Two discriminance,a sufficient and necessary condition for determining the nonsingularity and the diagonalization of bFLDCMrwcre discussed.Finally,by using Sherman-Morrison-Woodbury formula,the direct algorithm for solving r-circulant tridiagonal block systems of linear equations was provided.

关 键 词：块首尾差r-循环矩阵 判别法 对角化 直接算法 

分 类 号：O151.2[理学—数学]