Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

The aim of this paper is to establish explicit representations of the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, which covers the case when the generalized Schur complement is equal to zero.     

A note on the perturbation of an outer inverse

In this note, we present an explicit formula for perturbations of an outer inverse under certain conditions, which extends previous results. The second author was supported by the National Natural Science Foundation of China under grant 10871051 and the Shanghai Education Committee under grant 08511501703.     

Iterative refinement of computing inverse matrix

This work discusses the iterative refinement for finding the numerical inverse of a given non-singular matrix. The algorithm and convergence analysis of the iterative procedures are presented. Numerical examples are given to show the effectiveness of the iterative refinement.     

A perturbation approach for a type of inverse linear programming problems

We consider an inverse linear programming (LP) problem in which the parameters in both the objective function and the constraint set of a given LP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear complementarity constrained minimization problem. With the help of the smoothed Fischer–Burmeister function, we propose a perturbation approach to solve the inverse problem and demonstrate its global convergence. An inexact Newton method is constructed to solve the perturbed problem and numerical results are reported to show the effectiveness of the approach.     

三类保辛摄动及其数值比较

摄动法近似应当保辛．本文指出,有限元位移法自动保辛,有限元混合能表示也保辛．摄动法的刚度阵Taylor级数展开能证明保辛;混合能的Taylor级数展开摄动也证明了保辛．但传递辛矩阵的Taylor级数展开摄动却不能保辛．辛矩阵只能在乘法群下保辛,故传递辛矩阵的保辛摄动必须采用正则变换的乘法．虽然刚度阵加法摄动、混合能矩阵加法摄动与传递辛矩阵正则变换乘法摄动都保辛,但这3种摄动近似并不相同．最后通过数值例题给出了对比．     

一般阻尼动力系统非奇异摄动法

借助矩阵摄动理论,将模态叠加法运用于一般阻尼矩阵的动力学方程求解结构的动响应是一种较为理想的方法.但当系统的外荷载激振频率接近于系统的固有频率时,直接将阻尼矩阵作为摄动矩阵,会使解产生奇异,并导致求解失败或误差过大,这是因为模态坐标下的动力学方程是无阻尼方程.为了解决这一问题,本文考虑在模态坐标的动力学方程中保留一定的阻尼.即将阻尼做分解,代入振动方程,得到不同阶次摄动方程,再将摄动方程变换到模态坐标,即采用非奇异摄动方法.最后通过数值算例,得到一阶、二阶摄动,将其与精确解进行比较.精度明显得到改善,基本趋于精确解.从而验证了本方法的精确性和有效性.     

New perturbation analysis for generalized saddle point systems

In this paper we present perturbation bounds and condition numbers for the generalized saddle point system. Numerical results are also given. The work of Li was supported in part by National Natural Science Foundation of China (No. 10671077) and Guangdong Provincial Natural Science Foundations (06025061), P.R. China.     

小参数摄动法与保辛

应用数学与力学经常使用小参数摄动近似．在物理与力学中有大量保守体系的分析．保守体系的特点是保辛．本文指出小参数摄动法保辛的问题应予考虑．位移法摄动是保辛的,而辛矩阵的加法摄动则未能保辛．数值例题给出了对比．     

AVS反扫描、反量化和反变换模块的一种优化设计

根据AVS标准中的反扫描、反量化和反变换算法特点提出了一种用于AVS解码芯片中的反扫描、反量化和反变换硬件模块的设计方案,该设计以宏块为单位进行操作,便于集成到整个解码芯片的流水线中。同时,在宏块内实现了8×8子块的流水线操作并进行了优化,在反变换中用RAM代替寄存器堆进行转置操作。综合结果表明,该设计在获得了较高处理速度的同时节省了大量的寄存器和选择器资源。     

行满秩Toeplitz型矩阵Moore-Penrose逆的快速算法

通过构造对称分块矩阵给出了秩为m的m×n阶Toeplitz型矩阵Moore-Penrose逆的快速算法。该算法计算复杂度为O（mn）+O（m²）,而由T^T（TT^T）^-1直接求解所需运算量为O（m²n）+O（m3）。数值算例表明了该快速算法的有效性。     

Some results on the Drazin inverse of a modified matrix

We give new conditions under which the Drazin inverse of a modified matrix $A-CD^DB$ can be expressed in terms of the Drazin inverse of $A$ and its generalized Schur complement $Z=D-BA^DC$ , generalizing some recent results in the literature.     

Regular factorizations and perturbation analysis for the core inverse of linear operators in Hilbert spaces

ABSTRACT

This paper concerns the regular factorization and expression of the core inverse in a Hilbert space. Utilizing the regular factorization, we first give some characterizations for the existence and the expression of the group inverse and core inverse. Based on these, we prove that the core inverse of the perturbed operator has the simplest possible expression if and only if the perturbation is range-preserving, and derive an explicit expression under the rank-preserving perturbation. Thus we can conclude that both the range-preserving perturbation and the rank-preserving perturbation are all continuous perturbations. The obtained results extend and improve many recent ones in matrix theory and operator theory.     

Some representations for the Drazin inverse of a modified matrix

In this paper, we give some results for the Drazin inverse of a modified matrix \(M=A-CD^dB\) with the generalized Schur complement \(Z=D-BA^dC\) under some conditions. Further, we present some new results for the Drazin inverse of the modified matrix \(M=A-CD^dB\) , when the generalized Schur complement \(Z=0\) under some conditions. As a result, some conclusions are obtained directly from our results.     

求解弱非比例阻尼系统实模态解的阻尼矩阵摄动法

提出了一种求解弱非比例阻尼振动系统实模态解的摄动方法和将非比拟阻尼矩阵分解为比例阻尼矩阵和余项阻尼矩阵的方法.对于弱非比例阻尼振动系统,通过同时对阻尼矩阵和响应矢量进行小参数摄动,将原非比例阻尼系统分解为一系列的比例阻尼振动系统,在此基础上用正则模态变换将各阶比例阻尼的摄动方程解耦,从而求得原非比例阻尼振动系统的近似解析解.计算实例表明,此方法的结果与数值计算结果十分吻合.     

奇异系统能量受限的输出调节通过一般状态反馈的可解性

本文讨论奇异系统的能量受限的输出调节问题。在不考虑闭环正则化约束的情况下，得到了通过一般状态反馈来实现这种输出调节的充要条件。     

The extended homotopy perturbation method for the boundary layer flow due to a stretching sheet with partial slip

A fully analytical solution of the steady, laminar and axisymmetric flow of a Newtonian fluid due to a stretching sheet when there is a partial slip of the fluid past the sheet has been derived using the extended homotopy perturbation method. The solution differs from that obtained by the classical homotopy perturbation method in that it is capable of generating a totally analytical solution up to any desired degree of accuracy and is not limited to the first-order correction terms. For an eight-decimal accuracy, it is sufficient to take 12 terms in the power series in the perturbation parameter, provided that use is made of Shanks’ transformation. Unlike other similar problems involving mass transfer across the sheet and/or the presence of a transverse magnetic field, the solution for the present problem is relatively insensitive to the velocity slip parameter.