广义Bott-Duffin逆及加权Drazin逆的若干性质

本文给出了L-零矩阵的广义Bott-Duffin逆及矩阵的加权Drazin逆的若干性质及表达形式．     

四元数矩阵的加权广义逆

利用四元数矩阵的加权奇异值分解 ,给出了四元数矩阵加权广义逆的显式表达 ,简化了应瓦金给出的相应结果 ,同时解答了有关的公开问题 .     

A Finite Method for Computing the Drazin and Core-EP Inverses of Matrices Based on Partial Full-Rank Factorization

This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically ex-tends the classic full-rank factorization method for computing the Drazin in-verses established by R.E.Cline.The result is then extended to the core-EP inverses.     

矩阵的加权Moore—Penrose逆

利用矩阵的广义奇异值分解，给出了复数域上矩阵的Moore—Penrose逆存在的充要条件及其表达式．     

Fuzzy矩阵的加权Moore-Penrose逆

给出了Fuzzy矩阵加权Moore-Penrose逆AM+N的定义,研究了Fuzzy矩阵加权Moore-Penrose逆AM+N的存在性问题,证明了当权矩阵M,N满足一定条件时,AM+N存在且A+MN=AT的充要条件是ANATMA≤A,推广了Fuzzy矩阵和Boolean矩阵的相应结果.     

正则环上矩阵的加权广义逆

定义了正则环上矩阵的加权广义逆,得到其存在的充要条件和表达式,推广了以往文献的相应结果.     

分块算子矩阵的加权EP

本文在加权广义Schur补的基础上, 引入并研究了Hilbert空间上分块算子矩阵的加权Moore-Penrose逆和加权EP. 进一步, 给出了加权EP算子在算子方程中的一个应用.     

M-P逆和加权M-P逆的有限迭代计算公式

本文，对于任意给定的矩阵A，我们给出了计算其M—P逆和加权M—P逆的有限迭代计算公式．根据这一迭代公式，当我们选取初始矩阵为X0=A^#，则矩阵A的加权M—P逆A^＋MN在不考虑舍入误差的情况下，可以在有限迭代的情况得到，同样当我们选取初始矩阵X0=A^＊，其M—P逆A^＋亦可以在有限迭代下获得．最后我们用数值例子检验了我们算法的正确性。     

乘法半群上的线性方程组与晶体对势的反演

用乘法半群上的线性方程组来求解晶体原子间对势反演的逆问题.这种方法是解决此类问题的一般性方法.本文还给出了一个计算实例.     

一类线性流形上矩阵方程X^TAX=B的反问题

设Ω={A∈ASR^nxn｜Ax=C，↓Ax∈RT（S），SS^＋C=0，T2^TC2=-C2^TT2，C2T2^＋72=C2}，考虑问题Ⅰ：给定X∈R^nxm，B∈R^mxm求A∈Ω，使得f（A）=｜｜X^TAX—B｜｜=min；问题Ⅱ：给定A^＋∈R^nxm，求A∈SE，使得｜｜A^＋-A｜｜=minA∈SE｜｜A^＋-A｜｜，SE是问题Ⅰ的解集。本文给出了问题Ⅰ、Ⅱ的解的通式，并给出了问题Ikf（A）=0成立的充分必要条件。     

Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product

In this paper,we extend the notion of the T-Schur decomposition to the weighted T-core-EP decomposition.Next,the weighted T-core-EP inverse of rectangular tensors is defined by a system,and its existence and uniqueness are obtained.Furthermore,the perturbation of the weighted T-core-EP inverse is studied under several conditions,and the relevant examples are provided to verify the perturbation bounds of the weighted T-core-EP inverse of tensors.     

A Class of Constrained Inverse Eigenproblem and Associated Approximation Problem for Symmetric Reflexive Matrices

Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived.     

环上矩阵的Moore-Penrose逆

本文研究环上矩阵的广义逆,得到其存在的充要条件,给出它的表达式,推广了以往文献的相应结果。     

等差-等比循环矩阵的逆矩阵求法

本文给出了等差-等此循环矩阵的逆矩阵求法,推广文[5]的结果.     

关于环上矩阵的群逆与Drazin逆

本文给出了环上一类方阵有群逆，｛１，５｝－道的充要条件及其它们的表式，推广了体（域）上关于群逆的Ｃｌｉｎｅ定理．此外还首次得到了矩阵有Ｄｒａｚｉｎ逆的判别准则及其它的表式．     

线性流形上广义次对称矩阵的左右逆特征值问题

研究线性流形上广义次对称矩阵的左右逆特征值问题及其最佳逼近问题.利用广义次对称矩阵的性质及矩阵的奇异值分解得到问题的通解表达式.同时,给出其有唯一的最佳逼近解以及求最佳逼近解的算法.     

The Cayley Method and the Inverse Eigenvalue Problem for Toeplitz Matrices

Despite the fact that symmetric Toeplitz matrices can have arbitrary eigenvalues, the numerical construction of such a matrix having prescribed eigenvalues remains to be a challenge. A two-step method using the continuation idea is proposed in this paper. The first step constructs a centro-symmetric Jacobi matrix with the prescribed eigenvalues in finitely many steps. The second step uses the Cayley transform to integrate flows in the linear subspace of skew-symmetric and centro-symmetric matrices. No special geometric integrators are needed. The convergence analysis is illustrated for the case of n = 3. Numerical examples are presented.     

加权广义逆矩阵的反序律

研究了在权数矩阵M,N可逆的条件下加权广义逆的反序律,给出了多种表达式.     

线性方程组的反问题

给定线性方程组AX= b,易求其通解,设为U0+ k1U1+ …+ krUr ()反过来,当给定()式,怎样构造一个线性方程组以()为通解? 本文称这类问题为线性方程组的反问题,并给出了这类问题的一个解法.     

线性方程组的异步松弛迭代法*

本文考虑解线性方程组经典迭代法的异步形式,对系数矩阵为H矩阵,给出了异步迭代过程收敛性的充分条件,这不仅降低了文献[3]对系数矩阵的要求,而且收敛区域比文献[3]的大.