**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**225

# Search results for: Q and R matrices

##### 225 Sign Pattern Matrices that Admit P0 Matrices

**Authors:**
Ling Zhang,
Ting-Zhu Huang

**Abstract:**

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

**Keywords:**
Sign pattern matrices,
P0 matrices,
graph,
digraph.

##### 224 On the Construction of Lightweight Circulant Maximum Distance Separable Matrices

**Authors:**
Qinyi Mei,
Li-Ping Wang

**Abstract:**

**Keywords:**
Linear diffusion layer,
circulant matrix,
lightweight,
MDS matrix.

##### 223 A Note on Toeplitz Matrices

**Authors:**
Hsuan-Chu Li

**Abstract:**

**Keywords:**
Toeplitz matrices,
LU factorization,
inverse of amatrix.

##### 222 Determination of Q and R Matrices for Optimal Pitch Aircraft Control

**Authors:**
N. Popovich,
P. Yan

**Abstract:**

**Keywords:**
Aircraft,
control,
digital,
optimal,
Q and R matrices

##### 221 Bisymmetric, Persymmetric Matrices and Its Applications in Eigen-decomposition of Adjacency and Laplacian Matrices

**Authors:**
Mahdi Nouri

**Abstract:**

**Keywords:**
Graphs theory,
Eigensolution,
adjacency and
Laplacian matrix,
Canonical forms,
bisymmetric,
per symmetric.

##### 220 Agents Network on a Grid: An Approach with the Set of Circulant Operators

**Authors:**
Babiga Birregah,
Prosper K. Doh,
Kondo H. Adjallah

**Abstract:**

**Keywords:**
Pascal matrices,
Binomial Recursion,
Circulant Operators,
Square Matrix Bipartition,
Local Network,
Parallel networks
of agents.

##### 219 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

**Authors:**
Mahdi Nouri

**Abstract:**

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

**Keywords:**
Riccati,
matrix equation,
eigenvalue problem,
symmetric,
bisymmetric,
persymmetric,
decomposition,
canonical
forms,
Graphs theory,
adjacency and Laplacian matrices.

##### 218 On Some Properties of Interval Matrices

**Authors:**
K. Ganesan

**Abstract:**

**Keywords:**
Interval arithmetic,
Interval matrix,
linear equations.

##### 217 Reconstruction of Binary Matrices Satisfying Neighborhood Constraints by Simulated Annealing

**Authors:**
Divyesh Patel,
Tanuja Srivastava

**Abstract:**

This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

**Keywords:**
Discrete Tomography,
exactly-1-4-adjacency,
simulated annealing.

##### 216 Iterative Solutions to Some Linear Matrix Equations

**Authors:**
Jiashang Jiang,
Hao Liu,
Yongxin Yuan

**Abstract:**

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

**Keywords:**
Matrix equation,
iterative algorithm,
parameter estimation,
minimum norm solution.

##### 215 Minimization Problems for Generalized Reflexive and Generalized Anti-Reflexive Matrices

**Authors:**
Yongxin Yuan

**Abstract:**

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.

**Keywords:**
approximation,
generalized reflexive matrix,
generalized
anti-reflexive matrix,
inverse eigenvalue problem.

##### 214 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.

##### 213 Effect of Steel Fibers on Flexural Behavior of Normal and High Strength Concrete

**Authors:**
K. M. Aldossari,
W. A. Elsaigh,
M. J. Shannag

**Abstract:**

An experimental study was conducted to investigate the effect of hooked-end steel fibers on the flexural behavior of normal and high strength concrete matrices. The fibers content appropriate for the concrete matrices investigated was also determined based on flexural tests on standard prisms. Parameters investigated include: matrix compressive strength ranging from 45 MPa to 70 MPa, corresponding to normal and high strength concrete matrices respectively; fibers volume fraction including 0, 0.5%, 0.76% and 1%, equivalent to 0, 40, 60, and 80 kg/m^{3} of hooked-end steel fibers respectively. Test results indicated that flexural strength and toughness of normal and high strength concrete matrices were significantly improved with the increase in the fibers content added; whereas a slight improvement in compressive strength was observed for the same matrices. Furthermore, the test results indicated that the effect of increasing the fibers content was more pronounced on increasing the flexural strength of high strength concrete than that of normal concrete.

**Keywords:**
Concrete,
flexural strength,
toughness,
steel fibers.

##### 212 The Projection Methods for Computing the Pseudospectra of Large Scale Matrices

**Authors:**
Zhengsheng Wang,
Xiangyong Ji,
Yong Du

**Abstract:**

**Keywords:**
Pseudospectra,
eigenvalue,
projection method,
Arnoldi,
IOM(q)

##### 211 The Inverse Eigenvalue Problem via Orthogonal Matrices

**Authors:**
A. M. Nazari,
B. Sepehrian,
M. Jabari

**Abstract:**

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

**Keywords:**
Householder matrix,
nonnegative matrix,
Inverse eigenvalue problem.

##### 210 The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data

**Authors:**
Jiashang Jiang,
Yongxin Yuan

**Abstract:**

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

**Keywords:**
Model updating,
damped gyroscopic system,
partially prescribed spectral information.

##### 209 Algorithm for Reconstructing 3D-Binary Matrix with Periodicity Constraints from Two Projections

**Authors:**
V. Masilamani,
Kamala Krithivasan

**Abstract:**

We study the problem of reconstructing a three dimensional binary matrices whose interiors are only accessible through few projections. Such question is prominently motivated by the demand in material science for developing tool for reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested to reconstruct 3D-object (crystalline structure) by reconstructing slice of the 3D-object. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. Formally, 3Dobject (crystalline structure) having a priory information is modeled by a class of 3D-binary matrices satisfying a priori information. We consider 3D-binary matrices with periodicity constraints, and we propose a polynomial time algorithm to reconstruct 3D-binary matrices with periodicity constraints from two orthogonal projections.

**Keywords:**
3D-Binary Matrix Reconstruction,
Computed Tomography,
Discrete Tomography,
Integral Max Flow Problem.

##### 208 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

**Authors:**
Jing Li,
Guang Zhou

**Abstract:**

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

**Keywords:**
Hadamard product,
Fan product; nonnegative matrix,
M-matrix,
Spectral radius,
Minimum eigenvalue,
1-path cover.

##### 207 Stability of a Special Class of Switched Positive Systems

**Authors:**
Xiuyong Ding,
Lan Shu,
Xiu Liu

**Abstract:**

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

**Keywords:**
Linear co-positive Lyapunov functions,
positive systems,
switched systems.

##### 206 On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays

**Authors:**
Xiu Liu,
Shouming Zhong,
Xiuyong Ding

**Abstract:**

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

**Keywords:**
Common linear co-positive Lyapunov functions,
positive systems,
switched systems,
delays.

##### 205 Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices

**Authors:**
Geng Yuan,
Yiwan Guo,
Fahui Zhai,
Shuhua Zhang

**Abstract:**

**Keywords:**
Quaternionic matrix,
left spectrum,
linear preserver
map.

##### 204 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices

**Authors:**
Khosrow Maleknejad,
Yaser Rostami

**Abstract:**

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

**Keywords:**
Integro-differential equations,
Quartic B-spline
wavelet,
Operational matrices.

##### 203 Buckling of Plates on Foundation with Different Types of Sides Support

**Authors:**
Ali N. Suri,
Ahmad A. Al-Makhlufi

**Abstract:**

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.

The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.

To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.

Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.

The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.

The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

**Keywords:**
Buckling,
Finite Strip,
Different Sides Support,
Plates on Foundation.

##### 202 The Orlicz Space of the Entire Sequence Fuzzy Numbers Defined by Infinite Matrices

**Authors:**
N.Subramanian,
C.Murugesan

**Abstract:**

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

**Keywords:**
Fuzzy numbers,
infinite matrix,
Orlicz space,
entiresequence.

##### 201 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion

**Authors:**
Aki Happonen,
Adrian Burian,
Erwin Hemming

**Abstract:**

**Keywords:**
Cholesky Decomposition,
Fixed-point,
Matrix
inversion,
Reconfigurable processing.

##### 200 Structural Damage Detection via Incomplete Modal Data Using Output Data Only

**Authors:**
Ahmed Noor Al-Qayyim,
Barlas Ozden Caglayan

**Abstract:**

**Keywords:**
Damage detection,
two points–condensation,
structural health monitoring,
signals processing,
optimization.

##### 199 Some New Upper Bounds for the Spectral Radius of Iterative Matrices

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

**Abstract:**

**Keywords:**
doubly α diagonally dominant matrix,
eigenvalue,
iterative matrix,
spectral radius,
upper bound.

##### 198 A Note on the Convergence of the Generalized AOR Iterative Method for Linear Systems

**Authors:**
Zhong-xi Gao,
Hou-biao Li

**Abstract:**

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

**Keywords:**
Diagonally dominant matrix,
GAOR method,
Linear
system,
Convergence

##### 197 The Effects of a Thin Liquid Layer on the Hydrodynamic Machine Rotor

**Authors:**
Jaroslav Krutil,
František Pochylý,
Simona Fialová,
Vladimír Habán

**Abstract:**

**Keywords:**
Computational modeling,
mathematical model,
hydrodynamic gap,
matrices of mass,
stiffness and damping.

##### 196 Some Applications of Transition Matrices via Eigen Values

**Authors:**
Adil AL-Rammahi

**Abstract:**

In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages.

**Keywords:**
Eigen value problem,
transition matrix,
state vector,
information theory.