**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**43

# Search results for: Eigenvalues

##### 43 Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions

**Authors:**
I. Otete,
A. I. Ejere,
I. S. Okunzuwa

**Abstract:**

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

**Keywords:**
Schrödinger's equation,
bound state,
Hulthen-Yukawa potential,
Nikiforov-Uvarov,
D-dimensions

##### 42 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

**Authors:**
Lokendra K. Balyan

**Abstract:**

**Keywords:**
Schur Factorization,
Eigenvalues of nonsymmetric matrix,
Orthoganal matrix.

##### 41 Eigenvalues of Particle Bound in Single and Double Delta Function Potentials through Numerical Analysis

**Authors:**
Edward Aris D. Fajardo,
Hamdi Muhyuddin D. Barra

**Abstract:**

**Keywords:**
Double Delta Potential,
Eigenstates,
Eigenvalue,
Numerov Method,
Single Delta Potential

##### 40 Matrix Valued Difference Equations with Spectral Singularities

**Authors:**
Serifenur Cebesoy,
Yelda Aygar,
Elgiz Bairamov

**Abstract:**

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

**Keywords:**
Difference Equations,
Jost Functions,
Asymptotics,
Eigenvalues,
Continuous Spectrum,
Spectral Singularities.

##### 39 Some New Bounds for a Real Power of the Normalized Laplacian Eigenvalues

**Authors:**
Ayşe Dilek Maden

**Abstract:**

For a given a simple connected graph, we present some new bounds via a new approach for a special topological index given by the sum of the real number power of the non-zero normalized Laplacian eigenvalues. To use this approach presents an advantage not only to derive old and new bounds on this topic but also gives an idea how some previous results in similar area can be developed.

**Keywords:**
Degree Kirchhoff index,
normalized Laplacian
eigenvalue,
spanning tree.

##### 38 Human Face Detection and Segmentation using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

**Authors:**
J. Prakash,
K. Rajesh

**Abstract:**

**Keywords:**
Circular Hough Transform,
Covariance matrix,
Eigenvalues,
Elliptical Hough Transform,
Face segmentation,
Raster
Scan Algorithm.

##### 37 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 36 A Novel Approach for Coin Identification using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

**Authors:**
J. Prakash,
K. Rajesh

**Abstract:**

**Keywords:**
Circular Hough Transform,
Coin detection,
Covariance matrix,
Eigenvalues,
Raster scan Algorithm,
Texton.

##### 35 On Detour Spectra of Some Graphs

**Authors:**
S.K.Ayyaswamy,
S.Balachandran

**Abstract:**

**Keywords:**
Detour eigenvalue (of a graph),
detour spectrum(of a graph),
detour energy(of a graph),
detour - equienergetic graphs.

##### 34 A Time-Reducible Approach to Compute Determinant |I-X|

**Authors:**
Wang Xingbo

**Abstract:**

*X*| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-

*X*|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix

*X*. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

**Keywords:**
Algorithm,
determinant,
computation,
eigenvalue,
time complexity.

##### 33 Multi-Rate Exact Discretization based on Diagonalization of a Linear System - A Multiple-Real-Eigenvalue Case

**Authors:**
T. Sakamoto,
N. Hori

**Abstract:**

**Keywords:**
Multi-rate discretization,
linear systems,
triangularization,
similarity transformation,
diagonalization,
exponential transformation,
multiple eigenvalues

##### 32 Automatic Generation Control Design Based on Full State Vector Feedback for a Multi-Area Energy System Connected via Parallel AC/DC Lines

**Authors:**
Gulshan Sharma

**Abstract:**

This article presents the design of optimal automatic generation control (AGC) based on full state feedback control for a multi-area interconnected power system. An extra high voltage AC transmission line in parallel with a high voltage DC link is considered as an area interconnection between the areas. The optimal AGC are designed and implemented in the wake of 1% load perturbation in one of the areas and the system dynamic response plots for various system states are obtained to investigate the system dynamic performance. The pattern of closed-loop eigenvalues are also determined to analyze the system stability. From the investigations carried out in the work, it is revealed that the dynamic performance of the system under consideration has an appreciable improvement when a high voltage DC line is paralleled with an extra high voltage AC line as an interconnection between the areas. The investigation of closed-loop eigenvalues reveals that the system stability is ensured in all case studies carried out with the designed optimal AGC.

**Keywords:**
Automatic generation control,
area control error,
DC link,
optimal AGC regulator,
closed-loop eigenvalues.

##### 31 Using Spectral Vectors and M-Tree for Graph Clustering and Searching in Graph Databases of Protein Structures

**Authors:**
Do Phuc,
Nguyen Thi Kim Phung

**Abstract:**

**Keywords:**
Eigenvalues,
m-tree,
graph database,
protein
structure,
spectra graph theory.

##### 30 A Contribution to the Polynomial Eigen Problem

**Authors:**
Malika Yaici,
Kamel Hariche,
Tim Clarke

**Abstract:**

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

**Keywords:**
Eigenvalues/Eigenvectors,
Latent values/vectors,
Matrix fraction description,
State space description.

##### 29 Optical Signal-To-Noise Ratio Monitoring Based on Delay Tap Sampling Using Artificial Neural Network

**Authors:**
Feng Wang,
Shencheng Ni,
Shuying Han,
Shanhong You

**Abstract:**

With the development of optical communication, optical performance monitoring (OPM) has received more and more attentions. Since optical signal-to-noise ratio (OSNR) is directly related to bit error rate (BER), it is one of the important parameters in optical networks. Recently, artificial neural network (ANN) has been greatly developed. ANN has strong learning and generalization ability. In this paper, a method of OSNR monitoring based on delay-tap sampling (DTS) and ANN has been proposed. DTS technique is used to extract the eigenvalues of the signal. Then, the eigenvalues are input into the ANN to realize the OSNR monitoring. The experiments of 10 Gb/s non-return-to-zero (NRZ) on–off keying (OOK), 20 Gb/s pulse amplitude modulation (PAM4) and 20 Gb/s return-to-zero (RZ) differential phase-shift keying (DPSK) systems are demonstrated for the OSNR monitoring based on the proposed method. The experimental results show that the range of OSNR monitoring is from 15 to 30 dB and the root-mean-square errors (RMSEs) for 10 Gb/s NRZ-OOK, 20 Gb/s PAM4 and 20 Gb/s RZ-DPSK systems are 0.36 dB, 0.45 dB and 0.48 dB respectively. The impact of chromatic dispersion (CD) on the accuracy of OSNR monitoring is also investigated in the three experimental systems mentioned above.

**Keywords:**
Artificial neural network,
ANN,
chromatic dispersion,
delay-tap sampling,
optical signal-to-noise ratio,
OSNR.

##### 28 An Improved Adaptive Dot-Shape Beamforming Algorithm Research on Frequency Diverse Array

**Authors:**
Yanping Liao,
Zenan Wu,
Ruigang Zhao

**Abstract:**

Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues of the noise subspace, improve the divergence of small eigenvalues in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

**Keywords:**
Multi-carrier frequency diverse array,
adaptive beamforming,
correction index,
limited snapshot,
robust.

##### 27 Stiffness Modeling of 3-PRS Mechanism

**Authors:**
Xiaohui Han,
Yuhan Wang,
Jing Shi

**Abstract:**

**Keywords:**
3-PRS,
parallel mechanism,
stiffness analysis,
workspace.

##### 26 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.

##### 25 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

**Authors:**
Chao Yuan,
Bao Guang Tian

**Abstract:**

**Keywords:**
Generalized linear model,
generalized relative coefficient,
least eigenvalue,
relative efficiency.

##### 24 Information Entropy of Isospectral Hydrogen Atom

**Authors:**
Anil Kumar,
C. Nagaraja Kumar

**Abstract:**

**Keywords:**
Information Entropy,
BBM inequality,
Isospectral Potential.

##### 23 Local Stability of Equilibria: Leptospirosis

**Authors:**
Rujira Kongnuy

**Abstract:**

**Keywords:**
Eigenvalues,
Leptospirosis,
Local Stability,
Numerical Result

##### 22 Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems

**Authors:**
M. H. M. Rashid

**Abstract:**

**Keywords:**
Weyl’s theorem,
Weyl spectrum,
polaroid operators,
property (gm),
property (m).

##### 21 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)

##### 20 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.

##### 19 Turing Pattern in the Oregonator Revisited

**Authors:**
Elragig Aiman,
Dreiwi Hanan,
Townley Stuart,
Elmabrook Idriss

**Abstract:**

**Keywords:**
Diffusion driven instability,
common Lyapunov
function (CLF),
turing pattern,
positive-definite matrix.

##### 18 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.

##### 17 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

**Authors:**
R. B. Ogunrinde,
C. C. Jibunoh

**Abstract:**

**Keywords:**
Spectral decomposition,
eigenvalues of the Jacobian,
linear RHS,
homogeneous linear systems.

##### 16 An Eigen-Approach for Estimating the Direction-of Arrival of Unknown Number of Signals

**Authors:**
Dia I. Abu-Al-Nadi,
M. J. Mismar,
T. H. Ismail

**Abstract:**

A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

**Keywords:**
Array signal processing,
direction-of-arrival,
antenna arrays,
eigenvalues,
eigenvectors.

##### 15 Restarted GMRES Method Augmented with the Combination of Harmonic Ritz Vectors and Error Approximations

**Authors:**
Qiang Niu,
Linzhang Lu

**Abstract:**

Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.

**Keywords:**
Arnoldi process,
GMRES,
Krylov subspace,
systems of linear equations.

##### 14 A Hybrid Method for Determination of Effective Poles Using Clustering Dominant Pole Algorithm

**Authors:**
Anuj Abraham,
N. Pappa,
Daniel Honc,
Rahul Sharma

**Abstract:**

In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

**Keywords:**
Balanced truncation,
Clustering,
Dominant pole,
Hankel norm,
Model reduction.