**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1082

# Search results for: Singular matrix.

##### 1082 Semiconvergence of Alternating Iterative Methods for Singular Linear Systems

**Authors:**
Jing Wu

**Abstract:**

In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

**Keywords:**
Alternating iterative method,
Semiconvergence,
Singular
matrix.

##### 1081 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 1080 Enhancement of Low Contrast Satellite Images using Discrete Cosine Transform and Singular Value Decomposition

**Authors:**
A. K. Bhandari,
A. Kumar,
P. K. Padhy

**Abstract:**

**Keywords:**
Singular Value Decomposition (SVD),
discretecosine transforms (DCT),
image equalization and satellite imagecontrast enhancement.

##### 1079 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case

**Authors:**
Salim Ibrir

**Abstract:**

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

**Keywords:**
Singular systems,
Discrete-time systems,
Regularization,
LMIs

##### 1078 Optimal Placement of Piezoelectric Actuators on Plate Structures for Active Vibration Control Using Modified Control Matrix and Singular Value Decomposition Approach

**Authors:**
Deepak Chhabra,
Gian Bhushan,
Pankaj Chandna

**Abstract:**

The present work deals with the optimal placement of piezoelectric actuators on a thin plate using Modified Control Matrix and Singular Value Decomposition (MCSVD) approach. The problem has been formulated using the finite element method using ten piezoelectric actuators on simply supported plate to suppress first six modes. The sizes of ten actuators are combined to outline one actuator by adding the ten columns of control matrix to form a column matrix. The singular value of column control matrix is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with GA. Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions using Linear Quadratic regulator) scheme. It is observed that MCSVD approach has given the position of patches adjacent to each-other, symmetric to the centre axis and given greater vibration suppression than other previously published results on SVD.

**Keywords:**
Closed loop Average dB gain,
Genetic Algorithm (GA),
LQR Controller,
MCSVD,
Optimal positions,
Singular Value Decomposition (SVD) Approaches.

##### 1077 Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox

**Authors:**
Mehmet Bozca

**Abstract:**

**Keywords:**
Singular value,
optimisation,
gearbox,
torsional
vibration.

##### 1076 Some New Subclasses of Nonsingular H-matrices

**Authors:**
Guangbin Wang,
Liangliang Li,
Fuping Tan

**Abstract:**

In this paper, we obtain some new subclasses of non¬singular H-matrices by using a diagonally dominant matrix

**Keywords:**
H-matrix,
diagonal dominance,
a diagonally dominant matrix.

##### 1075 Encryption Image via Mutual Singular Value Decomposition

**Authors:**
Adil Al-Rammahi

**Abstract:**

Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

**Keywords:**
Image cryptography,
Singular values decomposition.

##### 1074 Parallel Multisplitting Methods for Singular Linear Systems

**Authors:**
Guangbin Wang,
Fuping Tan

**Abstract:**

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

**Keywords:**
Singular H-matrix,
linear systems,
extrapolated iterative method,
GMAOR method,
convergence.

##### 1073 An Algorithm for Computing the Analytic Singular Value Decomposition

**Authors:**
Drahoslava Janovska,
Vladimir Janovsky,
Kunio Tanabe

**Abstract:**

A proof of convergence of a new continuation algorithm for computing the Analytic SVD for a large sparse parameter– dependent matrix is given. The algorithm itself was developed and numerically tested in [5].

**Keywords:**
Analytic Singular Value Decomposition,
large sparse
parameter–dependent matrices,
continuation algorithm of a predictorcorrector
type.

##### 1072 On Certain Estimates Of Rough Oscillatory Singular Integrals

**Authors:**
H. M. Al-Qassem

**Abstract:**

We obtain appropriate sharp estimates for rough oscillatory integrals. Our results represent significant improvements as well as natural extensions of what was known previously.

**Keywords:**
Oscillatory singular integral,
Rough kernel,
Singular integral,
L^{p} boundedness.

##### 1071 Robust Fuzzy Control of Nonlinear Fuzzy Impulsive Singular Perturbed Systems with Time-varying Delay

**Authors:**
Caigen Zhou,
Haibo Jiang

**Abstract:**

**Keywords:**
T–S fuzzy model,
singular perturbed systems,
time-varying delay,
robust control.

##### 1070 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 1069 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 1068 Intensity of Singular Stress Field at the Corner of Adhesive Layer in Bonded Plate

**Authors:**
Nao-Aki Noda,
Yu Zhang,
Ken-Tarou Takaishi,
Hiroyuki Shibahara

**Abstract:**

**Keywords:**
Adhesive,
Adherent,
Intensity of singular stress,
Bonded strip

##### 1067 An Improved Algorithm for Calculation of the Third-order Orthogonal Tensor Product Expansion by Using Singular Value Decomposition

**Authors:**
Chiharu Okuma,
Naoki Yamamoto,
Jun Murakami

**Abstract:**

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

**Keywords:**
Singular value decomposition (SVD),
higher-orderSVD (HOSVD),
outer product expansion,
power method.

##### 1066 Positive Solutions of Second-order Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular equation.

##### 1065 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

**Authors:**
M. Abdulkawi,
Z. K. Eshkuvatov,
N. M. A. Nik Long

**Abstract:**

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

**Keywords:**
Singular integral equations,
Cauchy kernel,
Chebyshev polynomials,
interpolation.

##### 1064 Analysis of a Singular Perturbed Synchronous Generator with a Bond Graph Approach

**Authors:**
Gilberto Gonzalez-A,
Noe Barrera-G

**Abstract:**

**Keywords:**
Bond graph modelling,
synchronous generator,
singular perturbations

##### 1063 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation.

##### 1062 Effects of Geometry on Intensity of Singular Stress Fields at the Corner of Single-Lap Joints

**Authors:**
Yu Zhang,
Nao-Aki Noda,
Kentaro Takaishi

**Abstract:**

**Keywords:**
Adhesive thickness,
Overlap length,
Intensity ofsingular stress,
Single-lap joint

##### 1061 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 1060 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation.

##### 1059 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation

**Authors:**
Yongxin Yuan,
Hao Liu

**Abstract:**

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

**Keywords:**
Inverse problem,
Least-squares solution,
model updating,
Singular value decomposition (SVD),
Optimal approximation.

##### 1058 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 1057 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation

**Authors:**
Xiguang Li

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

**Keywords:**
Singular differential equation,
boundary value problem,
coin,
fixed point theory.

##### 1056 Elliptic Divisibility Sequences over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic divisibility sequences,
singular elliptic divisibilitysequences,
elliptic curves,
singular curves.

##### 1055 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 1054 The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem

**Authors:**
Gu-Fang Mou,
Ting-Zhu Huang

**Abstract:**

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

**Keywords:**
Matrix completion,
matrix completion,
N10 -matrix,
non-combinatorially symmetric,
cycle,
digraph.

##### 1053 Fuzzy Adjacency Matrix in Graphs

**Authors:**
Mahdi Taheri,
Mehrana Niroumand

**Abstract:**

**Keywords:**
Graph,
adjacency matrix,
fuzzy numbers