An efficient method for computing the inverse of arrowhead matrices

In this paper we propose a simple and effective method to find the inverse of arrowhead matrices which often appear in wide areas of applied science and engineering such as wireless communications systems, molecular physics, oscillators vibrationally coupled with Fermi liquid, and eigenvalue problems. A modified Sherman–Morrison inverse matrix method is proposed for computing the inverse of an arrowhead matrix. The effectiveness of the proposed method is illustrated and numerical results are presented along with comparative results.     

求m阶递推数列通项公式的两种方法

利用分析中的解析函数方法和代数中的矩阵方法,得到了m阶常系数齐次线性递推数列通项公式的解析表达式,是对已有结果的完善和推广.     

关于整数素因数间的一个新的对偶公式

主要目的是利用Liouville反转公式来给出整数素因数间的一个新的对偶公式,从而推广了K.Alladi的基于Mbius反转公式的对偶引理.     

除环上无限方阵的逆方阵

本文探讨了除环上无限方阵的逆方阵,得到了除环上无限方阵存在左（或右）逆方阵的充要条件．     

关于块有限无限方阵的非异性

利用有向图给出了块有限无限方阵的概念 ,得到了该类矩阵的置换相似标准形 ,以及该类矩阵非异性的一个充分必要条件 .     

A fast method to block-diagonalize a Hankel matrix

In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n ²) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.     

A polyominoes-permutations injection and tree-like convex polyominoes

Plane polyominoes are edge-connected sets of cells on the orthogonal lattice Z², considered identical if their cell sets are equal up to an integral translation. We introduce a novel injection from the set of polyominoes with n cells to the set of permutations of [n], and classify the families of convex polyominoes and tree-like convex polyominoes as classes of permutations that avoid some sets of forbidden patterns. By analyzing the structure of the respective permutations of the family of tree-like convex polyominoes, we are able to find the generating function of the sequence that enumerates this family, conclude that this sequence satisfies the linear recurrence an=6an−1−14an−2+16an−3−9an−4+2an−5, and compute the closed-form formula an=²n+2−(n³−n²+10n+4)/2.     

广义矩阵代数上的李导子

研究了广义矩阵代数上的一类李导子,证明了广义矩阵代数上李导子可以表示成一个导子和一个中心映射之和,并将这个结果应用到全矩阵代数上.     

convergence of the reconstruction formula for the potential function

It is known that the potential function of the Sturm-Liouville problem can be reconstructed from the nodal data by a pointwise limit. We show that this convergence is in fact .

     

分块带状矩阵的逆

1引言如果分块矩阵A=(A_(ij))_(n×n)满足A_(ij)=O(j-i＞p且i-j＞q),其中A_(ij)为m阶矩阵,则称A为(p,q)-分块带状矩阵．分块带状矩阵在一些实际问题中经常出现,例如在量子场论中用途很广的非线性Schr(?)dinger方程的差分离散问题,解热传导问题等,都会遇到分块带状矩阵．常见的分块三对角矩阵,分块五对角矩阵都是特殊的分块带状矩阵．采用通常的方法求解分块带状矩阵的逆矩阵时,需要进行O(n~3)次m阶矩阵的运算．本文首先将分块带状矩阵扩充成可逆的分块上(下)三角矩阵,利用其逆矩阵导出了分块带状矩阵的逆矩阵表达式;进而利用所得到的公式分别推导了分块三对角矩阵及分块五对角矩阵的逆矩阵的快速算法,所需运算量为O(n~2)次m阶矩阵的运算．本文的结果扩充了文[1]等关于分块三对角阵求逆的相关结果．     

关于第二类r-循环矩阵求逆的一种算法

利用矩阵的初等行变换给出可逆的第二类r-循环矩阵的求逆的简便算法．     

除环上无限方阵的分解

对除环上无限方阵的逆方阵作了简单讨论,证明了除环上无限方阵的分解定理．     

On the conditional increments of degradation processes

Recently, Wang and Xu (2010) developed an efficient EM algorithm for the semiparametric inference of the inverse Gaussian (IG) process. In the presence of missing degradation data, the algorithm needs to compute the mean of the IG increment during some time interval [_s1,_s2]$[s_1,s_2]$ conditional on that the process is tied down on two points before _s1$s_1$ and after _s2$s_2$, respectively. This study derives the conditional distribution of this increment and gives the expectation of the increment and of the reciprocal of the increment. The results simplify the implementation of the EM algorithm for the IG process. In a similar vein, we further derive distributions for the conditional increments of the Wiener process and the Gamma process, respectively.     

Biderivations of triangular algebras

Let be a triangular algebra. A bilinear map is called a biderivation if it is a derivation with respect to both arguments. In this paper we define the concept of an extremal biderivation, and prove that under certain conditions a biderivation of a triangular algebra is a sum of an extremal and an inner biderivation. The main result is then applied to (block) upper triangular matrix algebras and nest algebras. We also consider the question when a derivation of a triangular algebra is an inner derivation.     

计算周期三对角矩阵行列式和逆矩阵的新算法

给出了一种计算周期三对角矩阵行列式和逆矩阵的新递推算法,它们的运算复杂度分别为O(n)和O(n2),该算法是文献[5]和[6]中相关算法的拓广.     

上三角Toeplitz矩阵的一个结论

本文得出了上三角 Ｔｏｅｐｌｉｔｚ 矩阵关于矩阵乘法构成一交换群的结果,并给出其逆矩阵的计算方法．     

The inverse eigenvalue problem for symmetric quasi anti-bidiagonal matrices

In this paper we construct the symmetric quasi anti-bidiagonal matrix that its eigenvalues are given, and show that the problem is also equivalent to the inverse eigenvalue problem for a certain symmetric tridiagonal matrix which has the same eigenvalues. Not only elements of the tridiagonal matrix come from quasi anti-bidiagonal matrix, but also the places of elements exchange based on some conditions.