Search results for: Q and R matrices
225 Sign Pattern Matrices that Admit P0 Matrices
Authors: Ling Zhang, Ting-Zhu Huang
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1082
224 On the Construction of Lightweight Circulant Maximum Distance Separable Matrices
Authors: Qinyi Mei, Li-Ping Wang
Abstract:MDS matrices are of great significance in the design of block ciphers and hash functions. In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency. We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware. Furthermore, we provide circulant MDS matrices with as few bit XOR operations as possible for the classical dimensions 4 × 4, 8 × 8 over the space of linear transformations over finite field F42 . In contrast to previous constructions of MDS matrices, our constructions have achieved fewer XORs.
Keywords: Linear diffusion layer, circulant matrix, lightweight, MDS matrix.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 747
223 A Note on Toeplitz Matrices
Authors: Hsuan-Chu Li
Abstract:In this note, we demonstrate explicit LU factorizations of Toeplitz matrices for some small sizes. Furthermore, we obtain the inverse of referred Toeplitz matrices by appling the above-mentioned results.
Keywords: Toeplitz matrices, LU factorization, inverse of amatrix.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1079
222 Determination of Q and R Matrices for Optimal Pitch Aircraft Control
Authors: N. Popovich, P. Yan
Abstract:In this paper, the process of obtaining Q and R matrices for optimal pitch aircraft control system has been described. Since the innovation of optimal control method, the determination of Q and R matrices for such system has not been fully specified. The value of Q and R for optimal pitch aircraft control application, have been simulated and calculated. The suitable results for Q and R have been observed through the performance index (PI). If the PI is small “enough", we would say the Q & R values are suitable for that certain type of optimal control system. Moreover, for the same value of PI, we could have different Q and R sets. Due to the rule-free determination of Q and R matrices, a specific method is brought to find out the rough value of Q and R referring to rather small value of PI.
Keywords: Aircraft, control, digital, optimal, Q and R matricesProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1596
221 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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2305
220 Agents Network on a Grid: An Approach with the Set of Circulant Operators
Authors: Babiga Birregah, Prosper K. Doh, Kondo H. Adjallah
Abstract:In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems.
Keywords: Pascal matrices, Binomial Recursion, Circulant Operators, Square Matrix Bipartition, Local Network, Parallel networks of agents.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 993
219 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics
Authors: Mahdi Nouri
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1696
218 On Some Properties of Interval Matrices
Authors: K. Ganesan
Abstract:By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.
Keywords: Interval arithmetic, Interval matrix, linear equations.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1890
217 Reconstruction of Binary Matrices Satisfying Neighborhood Constraints by Simulated Annealing
Authors: Divyesh Patel, Tanuja Srivastava
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2328
216 Iterative Solutions to Some Linear Matrix Equations
Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1371
215 Minimization Problems for Generalized Reflexive and Generalized Anti-Reflexive Matrices
Authors: Yongxin Yuan
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 987
214 Some New Subclasses of Nonsingular H-matrices
Authors: Guangbin Wang, Liangliang Li, Fuping Tan
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 905
213 Effect of Steel Fibers on Flexural Behavior of Normal and High Strength Concrete
Authors: K. M. Aldossari, W. A. Elsaigh, M. J. Shannag
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/m3 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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1784
212 The Projection Methods for Computing the Pseudospectra of Large Scale Matrices
Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du
Abstract:The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.
Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1198
211 The Inverse Eigenvalue Problem via Orthogonal Matrices
Authors: A. M. Nazari, B. Sepehrian, M. Jabari
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  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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1451
210 The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data
Authors: Jiashang Jiang, Yongxin Yuan
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1638
209 Algorithm for Reconstructing 3D-Binary Matrix with Periodicity Constraints from Two Projections
Authors: V. Masilamani, Kamala Krithivasan
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4788
208 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices
Authors: Jing Li, Guang Zhou
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1782
207 Stability of a Special Class of Switched Positive Systems
Authors: Xiuyong Ding, Lan Shu, Xiu Liu
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1378
206 On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays
Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1282
205 Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices
Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang
Abstract:In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.
Keywords: Quaternionic matrix, left spectrum, linear preserver map.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 954
204 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices
Authors: Khosrow Maleknejad, Yaser Rostami
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2997
203 Buckling of Plates on Foundation with Different Types of Sides Support
Authors: Ali N. Suri, Ahmad A. Al-Makhlufi
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2034
202 The Orlicz Space of the Entire Sequence Fuzzy Numbers Defined by Infinite Matrices
Authors: N.Subramanian, C.Murugesan
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1072
201 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion
Authors: Aki Happonen, Adrian Burian, Erwin Hemming
Abstract:Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.
Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1535
200 Structural Damage Detection via Incomplete Modal Data Using Output Data Only
Authors: Ahmed Noor Al-Qayyim, Barlas Ozden Caglayan
Abstract:Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on to obtain very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. The study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using ‘Two Points Condensation (TPC) technique’. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices obtain from optimization the equation of motion using the measured test data. The current stiffness matrices compare with original (undamaged) stiffness matrices. The large percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element, where two cases consider. The method detects the damage and determines its location accurately in both cases. In addition, the results illustrate these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can be used also for big structures.
Keywords: Damage detection, two points–condensation, structural health monitoring, signals processing, optimization.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1904
199 Some New Upper Bounds for the Spectral Radius of Iterative Matrices
Authors: Guangbin Wang, Xue Li, Fuping Tan
Abstract:In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.
Keywords: doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1222
198 A Note on the Convergence of the Generalized AOR Iterative Method for Linear Systems
Authors: Zhong-xi Gao, Hou-biao Li
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, ConvergenceProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1193
197 The Effects of a Thin Liquid Layer on the Hydrodynamic Machine Rotor
Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán
Abstract:A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.
Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1439
196 Some Applications of Transition Matrices via Eigen Values
Authors: Adil AL-Rammahi
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2544