Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1009

Search results for: Eigenvalues of nonsymmetric matrix

1009 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

Authors: Lokendra K. Balyan

Abstract:

In this paper, we present an algorithm for computing a Schur factorization of a real nonsymmetric matrix with ordered diagonal blocks such that upper left blocks contains the largest magnitude eigenvalues. Especially in case of multiple eigenvalues, when matrix is non diagonalizable, we construct an invariant subspaces with few additional tricks which are heuristic and numerical results shows the stability and accuracy of the algorithm.

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

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1008 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.

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1007 Human Face Detection and Segmentation using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

Authors: J. Prakash, K. Rajesh

Abstract:

In this paper we propose a novel method for human face segmentation using the elliptical structure of the human head. It makes use of the information present in the edge map of the image. In this approach we use the fact that the eigenvalues of covariance matrix represent the elliptical structure. The large and small eigenvalues of covariance matrix are associated with major and minor axial lengths of an ellipse. The other elliptical parameters are used to identify the centre and orientation of the face. Since an Elliptical Hough Transform requires 5D Hough Space, the Circular Hough Transform (CHT) is used to evaluate the elliptical parameters. Sparse matrix technique is used to perform CHT, as it squeeze zero elements, and have only a small number of non-zero elements, thereby having an advantage of less storage space and computational time. Neighborhood suppression scheme is used to identify the valid Hough peaks. The accurate position of the circumference pixels for occluded and distorted ellipses is identified using Bresenham-s Raster Scan Algorithm which uses the geometrical symmetry properties. This method does not require the evaluation of tangents for curvature contours, which are very sensitive to noise. The method has been evaluated on several images with different face orientations.

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

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1006 A Novel Approach for Coin Identification using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

Authors: J. Prakash, K. Rajesh

Abstract:

In this paper we present a new method for coin identification. The proposed method adopts a hybrid scheme using Eigenvalues of covariance matrix, Circular Hough Transform (CHT) and Bresenham-s circle algorithm. The statistical and geometrical properties of the small and large Eigenvalues of the covariance matrix of a set of edge pixels over a connected region of support are explored for the purpose of circular object detection. Sparse matrix technique is used to perform CHT. Since sparse matrices squeeze zero elements and contain only a small number of non-zero elements, they provide an advantage of matrix storage space and computational time. Neighborhood suppression scheme is used to find the valid Hough peaks. The accurate position of the circumference pixels is identified using Raster scan algorithm which uses geometrical symmetry property. After finding circular objects, the proposed method uses the texture on the surface of the coins called texton, which are unique properties of coins, refers to the fundamental micro structure in generic natural images. This method has been tested on several real world images including coin and non-coin images. The performance is also evaluated based on the noise withstanding capability.

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

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1005 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.

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1004 On Detour Spectra of Some Graphs

Authors: S.K.Ayyaswamy, S.Balachandran

Abstract:

The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

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

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1003 A Time-Reducible Approach to Compute Determinant |I-X|

Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-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.

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1002 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.

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1001 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.

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1000 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.

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999 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

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998 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.

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997 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:

In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

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

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

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

Abstract:

This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

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

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995 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.

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994 Turing Pattern in the Oregonator Revisited

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

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

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

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993 Weighted Harmonic Arnoldi Method for Large Interior Eigenproblems

Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

Abstract:

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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992 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.

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991 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.

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990 Fuzzy Adjacency Matrix in Graphs

Authors: Mahdi Taheri, Mehrana Niroumand

Abstract:

In this paper a new definition of adjacency matrix in the simple graphs is presented that is called fuzzy adjacency matrix, so that elements of it are in the form of 0 and n N n 1 , ∈ that are in the interval [0, 1], and then some charactristics of this matrix are presented with the related examples . This form matrix has complete of information of a graph.

Keywords: Graph, adjacency matrix, fuzzy numbers

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989 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.

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988 Inverse Matrix in the Theory of Dynamic Systems

Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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987 Numerical Treatment of Matrix Differential Models Using Matrix Splines

Authors: Kholod M. Abualnaja

Abstract:

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

Keywords: Matrix Splines, Cubic Splines, Quartic Splines.

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986 On Positive Definite Solutions of Quaternionic Matrix Equations

Authors: Minghui Wang

Abstract:

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established.

Keywords: Matrix equation, Quaternionic matrix, Real representation, positive (semi)definite solutions.

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985 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

Authors: Won Sup Kim, Xue-Mei Cui, Seung Kee Han

Abstract:

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

Keywords: Chaotic oscillator, complex network, inverse coherence matrix, network estimation.

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984 Stiffness Modeling of 3-PRS Mechanism

Authors: Xiaohui Han, Yuhan Wang, Jing Shi

Abstract:

This paper proposed a stiffness analysis method for a 3-PRS mechanism for welding thick aluminum plate using FSW technology. In the molding process, elastic deformation of lead-screws and links are taken into account. This method is based on the virtual work principle. Through a survey of the commonly used stiffness performance indices, the minimum and maximum eigenvalues of the stiffness matrix are used to evaluate the stiffness of the 3-PRS mechanism. Furthermore, A FEA model has been constructed to verify the method. Finally, we redefined the workspace using the stiffness analysis method.

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

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983 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.

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

Authors: Mahdi Nouri

Abstract:

In this paper we introduce an efficient solution method for the Eigen-decomposition of bisymmetric and per symmetric matrices of symmetric structures. Here we decompose adjacency and Laplacian matrices of symmetric structures to submatrices with low dimension for fast and easy calculation of eigenvalues and eigenvectors. Examples are included to show the efficiency of the method.

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

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981 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords: Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius

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980 Optimal Design of Two-Channel Recursive Parallelogram Quadrature Mirror Filter Banks

Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

This paper deals with the optimal design of two-channel recursive parallelogram quadrature mirror filter (PQMF) banks. The analysis and synthesis filters of the PQMF bank are composed of two-dimensional (2-D) recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support region. The design problem can be facilitated by using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters. For finding the coefficients of the 2-D recursive NSHP DAFs, we appropriately formulate the design problem to result in an optimization problem that can be solved by using a weighted least-squares (WLS) algorithm in the minimax (L) optimal sense. The designed 2-D recursive PQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison.

Keywords: Parallelogram Quadrature Mirror Filter Bank, Doubly Complementary Filter, Nonsymmetric Half-Plane Filter, Weighted Least Squares Algorithm, Digital All-Pass Filter.

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