New method for computing the inverse of a matrix whose elements are linear combinations of Walsh functions

A new method is presented for computing the inverse of a matrix whose elements are linear combinations of Walsh functions. In this method, linear algebraic equation sets are derived to evaluate the Walsh coefficients of the elements in the inverse matrix. Since these equation sets have small dimensions and regular forms, the new method can be used efficiently, and is suitable for computer programming.     

Numerical simulation of a polysilicon thermal flexure actuator

 An electrothermal equation of a polysilicon thermal flexure actuator is presented, which takes heat conduction, air convection and radiation into account. A numerical method is developed to solve the equation. The deflection model based on the matrix displacement method, i.e. finite element method (FEM) in structural mechanics, is given. It transforms deflection equations into a matrix and is easy to calculate numerically. Simulation results for the actuator with typical dimensions are presented. Discussions are finally given. Received: 28 April 2000/Accepted: 9 January 2001     

Minimal parameter solution of the orthogonal matrix differentialequation

The straightforward solution of the first-order differential equation satisfied by all nth-order orthogonal matrices requires n² integrations to obtain the matrix elements. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation, and expressing the orthogonal matrix in terms of these parameters are considered in the present work. Several possibilities which are based on attitude determination in three dimensions are examined. It is concluded that not all 3-D methods have useful extensions to other dimensions, and that the 3-D Gibbs vector (or Cayley parameters) provide the most useful extension. An algorithm is developed using the resulting parameters, which are termed extended Rodrigues parameters, and numerical results are presented of the application of the algorithm to a fourth-order matrix     

Self-Repairing Algorithm of Lattice-Type Self-Reconfigurable Modular Robots

Self-reconfigurable modular robots consist of many identical modules. By changing the connections among modules, the configuration of the robot can be transformed into other configurations. For the self-reconfigurable modular robot, one of its main functions is its self-repairing ability. First, the module of the lattice-type self-reconfigurable robot is presented. It is composed of a central cube and six rotary arms. On each rotary arm the docking mechanism is designed to show the self-repairing ability. Second, the basic motion of the self-reconfigurable robot is described to change the positions of the module. The state matrix and the location matrix are proposed to describe the connection states. Third, a self-repairing algorithm based on the positions of the faulty modules is presented. The algorithm applies the Breadth-First-Search method and the Depth-First-Search method to find a locomotion path by which the faulty module is ejected and replaced by a spare module. At last, a simulation on the fourth-order lattice-type self-reconfigurable robot consisting of 729 modules shows the feasibility and effectiveness of this self-repairing algorithm in three dimensions.     

Efficient analysis of wireless communication antennas using an accurate [Z] matrix interpolation technique

An accurate impedance matrix interpolation technique based on the surface integral equation (SIE) is presented for the analysis of wireless communication antennas over wide frequency bands. The first‐order derivative of the impedance matrix at the internal frequency is considered in the cubic polynomial‐based interpolation scheme, thus the novel impedance matrix interpolation scheme will provide high accuracy and high efficiency over a frequency band. To demonstrate the efficiency and accuracy of the proposed method, numerical results for planar inverted F antennas (PIFA) and a wideband E‐shaped patch antenna are presented. Good agreement among the interpolation results, exact MoM solutions, finite element method (FEM) solutions, and measured data is observed over the bandwidth. Besides, dimensions of the feeding probe are also studied to investigate their effect on the input impedance and radiation patterns. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

An algorithm for the numerical solution of dense large general linear systems

An algorithm for the numerical solution of a dense large general linear system is presented. This algorithm is based on the Gauss elimination method. No special properties of the left side matrix are assumed and its dimensions depend only on the backing storage available. An error analysis is performed and a test example is given. Detailed documentation of the FORTRAN list appended, is also given.     

Computation of exterior potential fields by infinite substructuring

A numerical method is presented to evaluate approximate solutions of elliptic partial differential equations outside an arbitrary convex region. The exterior region is conceived as an infinite assembly of geometrically similar finite element cells. A complete set of spatially discretized shape functions is derived for the entire unbounded exterior within which Laplace's equation is required to be satisfied. These functions with the characteristic of outward decay are evaluated by solving a quadratic eigenproblem. The coefficient matrices therein are furnished by the finite element system matrix (which relates the resulting nodal fluxes to the corresponding field strengths) of a typical cell. Elements of that matrix are viewed in the light of the virtual work principle. The energy terms associated with any pair of those basic functions form a convergent geometrical series over a sequence of similarly shaped elements with increasing characteristic dimensions. The exact infinite sum of the virtual work quantities yields the elements of the boundary matrix for the unbounded region. This enables one to carry out the proposed infinite substructuring scheme over the entire infinite collection of those cells. Finally, an expression to estimate the exterior field at an arbitrary point is also presented. The present study has applications to elastostatic, hydrodynamic, electro- and magneto-static protentials in two and three dimensions.     

A new approach for multiple attribute group decision making with interval-valued intuitionistic fuzzy information

This paper proposes a novel method for multiple attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy information. The interval-valued intuitionistic fuzzy numbers of each expert preference matrix are first mapped into two dimensions. Thus, the values of each membership degree and non-membership degree are considered as points in the two-dimensional representation. Moreover, the distance between the points represents the variance among the different experts preferences. The preference points of the same character are considered as a point set. We employ the plant growth simulation algorithm (PGSA) to calculate the optimal rally points of every point set, the sum of whose Euclidean distances to other given points is minimal, and these optimal rally points reflect the preferences of the entire expert group. These points are used to establish an expert preference aggregation matrix. Suitable points from the matrix are chosen to constitute an ideal point matrix, a projection method is employed to calculate the sum of its Euclidean distance to the expert preference aggregation matrix, and the score of each alternative is evaluated. Finally, the overall ranking of alternatives is obtained. In addition, this study develops a process to evaluate the pros and cons of different aggregation methods. Two typical examples are presented to illustrate the feasibility and effectiveness of the proposed approach.     

Finding the transfer function of time invariant linear system without computing (sI - A)−1

A method is presented for hand calculation of the one-sided inverse of the transfer function matrix for time invariant linear systems. Unlike conventional methods, this procedure does not require the inversion of the matrix (sI - A). For single input single output systems, the procedure leads to a direct calculation of the transfer function. In the third part of this paper, we show how to use block matrix operations to reduce the dimensions of the matrices involved in the method. An example is given to illustrate the method.     

TLM analysis of a cylindrical metallic cavity excited with a real‐feed probe

The influence of feed‐probe dimensions on the resonant frequencies in a cylindrical metallic cavity is investigated and presented. Cavity modelling is achieved by using the transmission‐line matrix (TLM) time‐domain method and a wire node to account for the feed‐probe presence. The results of the TLM analysis are validated against the experimental results. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Multi-dimensional asymptotically stable finite difference schemes for the advection–diffusion equation

An algorithm is presented which solves the multi-dimensional advection–diffusion equation on complex shapes to second-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty-like terms. Numerical examples in two dimensions show that the method is effective even where standard schemes, stable by traditional definitions, fail. It gives accurate, non oscillatory results even when boundary layers are not resolved.     

Two-dimensional cache-oblivious sparse matrix-vector multiplication

In earlier work, we presented a one-dimensional cache-oblivious sparse matrix-vector (SpMV) multiplication scheme which has its roots in one-dimensional sparse matrix partitioning. Partitioning is often used in distributed-memory parallel computing for the SpMV multiplication, an important kernel in many applications. A logical extension is to move towards using a two-dimensional partitioning. In this paper, we present our research in this direction, extending the one-dimensional method for cache-oblivious SpMV multiplication to two dimensions, while still allowing only row and column permutations on the sparse input matrix. This extension requires a generalisation of the compressed row storage data structure to a block-based data structure, for which several variants are investigated. Experiments performed on three different architectures show further improvements of the two-dimensional method compared to the one-dimensional method, especially in those cases where the one-dimensional method already provided significant gains. The largest gain obtained by our new reordering is over a factor of 3 in SpMV speed, compared to the natural matrix ordering.     

Sequential decomposition of the matrix Riccati equation and its application to the linear quadratic regulator problem

The differential matrix Riccati equation for the multi-input-multi-output linear quadratic optimal regulator problem is considered. Two methods are presented, successive and parallel, that decompose this equation into a set of Riccati equations that correspond to optimal regulator problems of possibly reduced dimensions. The additivity of the solutions to the equations obtained by the successive sequential decomposition method (SDM) and the additivity of the inverses of the solutions to the equations obtained by the parallel SDM are established. Some duality relations between the successive and the parallel methods are presented via the use of the adjoint Riccati equation. The theory developed is extended to the algebraic matrix Riccati equation as a limiting case. The application of the SDMs in the infinite-time linear quadratic regulator problem is investigated. Special attention is paid to the partially ‘cheap’ problem where the cost of some of the regulator controls or of their combinations tends asymptotically to zero. Explicit expressions for the asymptotic optimal cost are derived and the behaviour of the asymptotic optimal root loci is investigated.     

Supervised two-step feature extraction for structured representation of text data

Training data matrix used for classification of text documents to multiple categories is characterized by large number of dimensions while the number of manually classified training documents is relatively small. Thus the suitable dimensionality reduction techniques are required to be able to develop the classifier. The article describes two-step supervised feature extraction method that takes advantage of projections of terms into document and category spaces. We propose several enhancements that make the method more efficient and faster than it was presented in our former paper. We also introduce the adjustment score that enables to correct defected targets or helps to identify improper training examples that bias extracted features.     

利用参数表示任意维数正交矩阵的ICA新算法

在独立分量分析 (Independent component analysis, ICA) 中, 寻找去除高阶相关的正交矩阵成为问题关键, 而正交矩阵具有特殊的空间结构, 组成它的每个列向量可视作 RN 中单位超球表面上一点, 当这些点彼此垂直时, 整体就组成一个正交矩阵. 自然地, 这些点可以用其球坐标来参数化. 本文通过观察正交矩阵的几何结构, 找到了任意维数的随机正交矩阵的参数表示方法, 且论证了这种表示的完备性; 同时, 对随机正交矩阵参数表示的随机性做了定量分析; 然后, 利用遗传算法对参数化正交矩阵中的参数进行搜索, 得到了分离结果. 本文称这种算法为 OICA 算法, 并给出了该算法的仿真实验.     

工程图矢量化中的尺寸识别与重建

尺寸识别是工程图识别的重要环节。针对现有单人口识别算法的局限性，提出了一种多人口的尺寸识别算法，从多种已识别的图形元素开始搜索一个尺寸标识。在遇到不能正常识别的图形元素时，通过先搜索其他组成元素获得尺寸标识的初步确认后，放宽阈值对未识别元素进行再识别，有效地识别受退化或干扰影响较大的尺寸元素。提出了基于坐标网络的图形元素尺寸重建方法，通过建立坐标网使每一尺寸在整体环境下得到调整，满足了图低复用对图形数据精确度的要求。     

Evaluating knowledge management capability of organizations: a fuzzy linguistic method

Knowledge management capability (KMC) is the source for organizations to gain the sustainable competitive advantage. KMC evaluation is a required work with strategic significance. However it still has not been addressed in the existing literatures. So the objective of this study is to investigate a fuzzy multiple attributes decision-making method (FMADM) for evaluating KMC. In this paper, a framework for evaluating KMC is presented, which includes two parts, one is an evaluation hierarchy with attributes, the other a judgment matrix model with two dimensions to identify the evaluation results of KMC. Then, a fuzzy linguistic approach is proposed to evaluate the KMC of organizations. The evaluation results of KMC obtained through the proposed approach are objective and unbiased due to two reasons. Firstly, the results are generated by a group of experts in the presence of motile attributes. Secondly, the fuzzy linguistic approach employed in this paper has more advantage to reduce distortion and losing of information than other fuzzy linguistic approaches. Through evaluation result of KMC, managers could judge the necessity to improve the KMC and determine which dimension of KMC is the most needed direction to improve. Additionally, an example is used to illustrate the availability of the proposed method.     

Three-dimensional static analysis,of a spatially loaded planar rigid-jointed plexus frame

An exact matrix solution for the static analysis of a multi-storey and multi-column rectangular rigid-jointed plexus frame, subjected to a general spatial loading, is presented. Since the obtained closed-form formulae, giving all the structure redundants, include matrices of maximum dimensions mn × mn (where m = number of storeys and n = number of columns), the proposed methodology is more convenient compared to other existing methods, because it requires less memory space and computer coding. Also, a numerical application demonstrates the correctness and the potentialities of the method. In addition, this solution technique may become a useful guideline for the further investigation of three-dimensional frame structures.     

Numerical integration of the time-dependent equations of motion for taylor vortex flow

A method is presented for the finite difference solution of the equations of fluid motion. The complete Navier-Stokes equations are expressed in terms of tangential velocity, vorticity and stream function. The transformed equations are solved using an alternating direction implicit scheme. The classical problem of hydrodynamic stability of the rotational Couette flow is solved in two dimensions. Comparison with other numerical and experimental works shows that the method reported here is computationally stable, even when used with coarse grids and relatively large time increments.     

Global Exponential Stability Analysis of Discrete‐Time Genetic Regulatory Networks with Time Delays

This paper focuses on the study of global robust exponential stability of discrete‐time genetic regulatory networks (GRNs) with time‐invariant/time‐varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality (LMI) approach, which needs to verify whether there exists a feasible solution of a set of LMIs. Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M‐matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete‐time GRNs with time‐invariant/time‐varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M‐matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.