The Explicit Expressions of Level-k Circulant Matrices of Type(n_1,n_2.…,n_k) and Their Some Properties

In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...     

Nonsingularity on Level-k (r_1, r_2,…, r_k)-circulant Matrices of Type (n_1, n_2,…, n_k)

0.IntroductionThecirculantmatricesareveryimportantandspecialmatrices.Duringmanylargecom-putationproblemsofsignaldealing,theoryphysicsandlookingforoil,weoftenmeetwiththenumericalcomputationproblemsofthesortsystem.Therefore,thestudiesofcirculantmatricesarenoticedbymanymathematicsexPerts.Consideringtheneedsofmanyrealisticcomputationproblems,itisgiventhatdefinitionoflevel-k(rl,rz,-.-,rk)-circulantmatricesoftyPe(n,,n2,...,nk)in[l]andstudieditssomeproperties,theMoore-Penroseinverseandgeneralizedin…     

Nonsingularity on Level—2（r1,r2）—circulant Matrices of Type（m,n）

ＮｏｎｓｉｎｇｕｌａｒｉｔｙｏｎＬｅｖｅｌ－２（ｒ_１，ｒ_２）－ｃｉｒｃｕｌａｎｔＭａｔｒｉｃｅｓｏｆＴｙｐｅ（ｍ，ｎ）ＪｉａｎｇＺｈａｏｌｉｎ（江兆林）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＬｉｎｙｉＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｓｈａｎｄｏｎｇ，Ｌｉｎ...     

一类比式和问题的全局优化方法

对于一类比式和问题(P)给出一全局优化算法.首先利用线性约束的特征推导出问题(P)的等价问题(P1),然后利用新的线性松弛方法建立了问题(P1)的松弛线性规划(RLP),通过对目标函数可行域线性松弛的连续细分以及求解一系列线性规划,提出的分枝定界算法收敛到问题(P)的全局最优解.最终数值实验结果表明了该算法的可行性和高效性.