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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16481081 Solving Linear Matrix Equations by Matrix Decompositions
Authors: Yongxin Yuan, Kezheng Zuo
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20521080 Enhancement of Low Contrast Satellite Images using Discrete Cosine Transform and Singular Value Decomposition
Authors: A. K. Bhandari, A. Kumar, P. K. Padhy
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In this paper, a novel contrast enhancement technique for contrast enhancement of a low-contrast satellite image has been proposed based on the singular value decomposition (SVD) and discrete cosine transform (DCT). The singular value matrix represents the intensity information of the given image and any change on the singular values change the intensity of the input image. The proposed technique converts the image into the SVD-DCT domain and after normalizing the singular value matrix; the enhanced image is reconstructed by using inverse DCT. The visual and quantitative results suggest that the proposed SVD-DCT method clearly shows the increased efficiency and flexibility of the proposed method over the exiting methods such as Linear Contrast Stretching technique, GHE technique, DWT-SVD technique, DWT technique, Decorrelation Stretching technique, Gamma Correction method based techniques.Keywords: Singular Value Decomposition (SVD), discretecosine transforms (DCT), image equalization and satellite imagecontrast enhancement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 38311079 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case
Authors: Salim Ibrir
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15891078 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
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30681077 Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox
Authors: Mehmet Bozca
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Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.Keywords: Singular value, optimisation, gearbox, torsional vibration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19401076 Some New Subclasses of Nonsingular H-matrices
Authors: Guangbin Wang, Liangliang Li, Fuping Tan
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10291075 Encryption Image via Mutual Singular Value Decomposition
Authors: Adil Al-Rammahi
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20781074 Parallel Multisplitting Methods for Singular Linear Systems
Authors: Guangbin Wang, Fuping Tan
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13451073 An Algorithm for Computing the Analytic Singular Value Decomposition
Authors: Drahoslava Janovska, Vladimir Janovsky, Kunio Tanabe
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14501072 On Certain Estimates Of Rough Oscillatory Singular Integrals
Authors: H. M. Al-Qassem
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13081071 Robust Fuzzy Control of Nonlinear Fuzzy Impulsive Singular Perturbed Systems with Time-varying Delay
Authors: Caigen Zhou, Haibo Jiang
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The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16901070 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp
Authors: Ahmet Tekcan
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Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.Keywords: Singular curve, elliptic curve, rational points.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14381069 On the Approximate Solution of a Nonlinear Singular Integral Equation
Authors: Nizami Mustafa, C. Ardil
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19111068 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
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In this paper the strength of adhesive joint under tension and bending is discussed on the basis of intensity of singular stress by the application of FEM. A useful method is presented with focusing on the stress at the edge of interface between the adhesive and adherent obtained by FEM. After analyzing the adhesive joint strength with all material combinations, it is found that to improve the interface strength, thin adhesive layers are desirable because the intensity of singular stress decreases with decreasing the thickness.Keywords: Adhesive, Adherent, Intensity of singular stress, Bonded strip
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14981067 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
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16831066 Positive Solutions of Second-order Singular Differential Equations in Banach Space
Authors: Li Xiguang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12381065 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type
Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16501064 Analysis of a Singular Perturbed Synchronous Generator with a Bond Graph Approach
Authors: Gilberto Gonzalez-A, Noe Barrera-G
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An analysis of a synchronous generator in a bond graph approach is proposed. This bond graph allows to determine the simplified models of the system by using singular perturbations. Firstly, the nonlinear bond graph of the generator is linearized. Then, the slow and fast state equations by applying singular perturbations are obtained. Also, a bond graph to get the quasi-steady state of the slow dynamic is proposed. In order to verify the effectiveness of the singularly perturbed models, simulation results of the complete system and reduced models are shown.Keywords: Bond graph modelling, synchronous generator, singular perturbations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16931063 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14601062 Effects of Geometry on Intensity of Singular Stress Fields at the Corner of Single-Lap Joints
Authors: Yu Zhang, Nao-Aki Noda, Kentaro Takaishi
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This paper discusses effects of adhesive thickness, overlap length and material combinations on the single-lap joints strength from the point of singular stress fields. A useful method calculating the ratio of intensity of singular stress is proposed using FEM for different adhesive thickness and overlap length. It is found that the intensity of singular stress increases with increasing adhesive thickness, and decreases with increasing overlap length. The increment and decrement are different depending on material combinations between adhesive and adherent.Keywords: Adhesive thickness, Overlap length, Intensity ofsingular stress, Single-lap joint
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17481061 On Generalized New Class of Matrix Polynomial Set
Authors: Ghazi S. Kahmmash
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12421060 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16701059 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
Authors: Yongxin Yuan, Hao Liu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16411058 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation
Authors: Li Xiguang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12951057 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation
Authors: Xiguang Li
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11221056 Elliptic Divisibility Sequences over Finite Fields
Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim
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In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.Keywords: Elliptic divisibility sequences, singular elliptic divisibilitysequences, elliptic curves, singular curves.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16971055 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation
Authors: Li Xiguang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14061054 The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem
Authors: Gu-Fang Mou, Ting-Zhu Huang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10791053 Fuzzy Adjacency Matrix in Graphs
Authors: Mahdi Taheri, Mehrana Niroumand
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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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