Search results for: iterative method
8040 A New Preconditioned AOR Method for Z-matrices
Authors: Guangbin Wang, Ning Zhang, Fuping Tan
In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.
Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1420
8039 Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices
Authors: Li Jiang, Baoguang Tian
Abstract:In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.
Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1084
8038 An Iterative Method for Quaternionic Linear Equations
Authors: Bin Yu, Minghui Wang, Juntao Zhang
By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.
Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1630
8037 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
Authors: Xingping Sheng
Abstract:Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.
Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1156
8036 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application
Authors: Minghui Wang
Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.
Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1370
8035 A New Iterative Method for Solving Nonlinear Equations
Authors: Ibrahim Abu-Alshaikh
In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.
Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1537
8034 Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method
Authors: Sachin Bhalekar, Varsha Daftardar-Gejji
Abstract:In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.
Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2082
8033 An Efficient Iterative Updating Method for Damped Structural Systems
Authors: Jiashang Jiang
Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.
Keywords: Model updating, iterative algorithm, damped structural system, optimal approximation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1221
8032 Approximating Fixed Points by a Two-Step Iterative Algorithm
Authors: Safeer Hussain Khan
In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.
Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1877
8031 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems
Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar
Abstract:In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.
Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equationsProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1360
8030 Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi
Abstract:We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.
Keywords: rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1696
8029 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation
Authors: Sarun Phibanchon
The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.
Keywords: soliton, iterative method, spectral method, plasmaProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1744
8028 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations
Authors: Osama Yusuf Ababneh
For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.
Keywords: Third-order convergence, non-linear equations, root finding, iterative method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2792
8027 Parallel Multisplitting Methods for Singular Linear Systems
Authors: Guangbin Wang, Fuping Tan
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 1116
8026 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices
Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao
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 radiusProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1156
8025 Iterative Methods for Computing the Weighted Minkowski Inverses of Matrices in Minkowski Space
Authors: Xiaoji Liu, Yonghui Qin
In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses AM,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations.
Keywords: iterative method, the Minskowski inverse, AProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1283
8024 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation
Authors: Minghui Wang, Luping Xu, Juntao Zhang
Abstract:In this paper, according to the classical algorithm LSQR for solving the least-squares problem, an iterative method is proposed for least-squares solution of constrained matrix equation. By using the Kronecker product, the matrix-form LSQR is presented to obtain the like-minimum norm and minimum norm solutions in a constrained matrix set for the symmetric arrowhead matrices. Finally, numerical examples are also given to investigate the performance.
Keywords: Symmetric arrowhead matrix, iterative method, like-minimum norm, minimum norm, Algorithm LSQR.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1175
8023 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation
Authors: N. Parandin, M. A. Fariborzi Araghi
Abstract:in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.
Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1288
8022 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 1194
8021 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices
Authors: Zhuan-de Wang, Hou-biao Li, Zhong-xi Gao
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1636
8020 A Comparative Study of High Order Rotated Group Iterative Schemes on Helmholtz Equation
Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping
Abstract:In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.
Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1036
8019 On the Solution of Fully Fuzzy Linear Systems
Authors: Hsuan-Ku Liu
A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
Keywords: Fully fuzzy linear equations, iterative method, homotopy perturbation method, approximate solutions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1615
8018 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems
Authors: Shengfeng Li, Rujing Wang
Abstract:In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.
Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1725
8017 Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations
Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat
Abstract:Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.
Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1770
8016 Iterative Clustering Algorithm for Analyzing Temporal Patterns of Gene Expression
Authors: Seo Young Kim, Jae Won Lee, Jong Sung Bae
Abstract:Microarray experiments are information rich; however, extensive data mining is required to identify the patterns that characterize the underlying mechanisms of action. For biologists, a key aim when analyzing microarray data is to group genes based on the temporal patterns of their expression levels. In this paper, we used an iterative clustering method to find temporal patterns of gene expression. We evaluated the performance of this method by applying it to real sporulation data and simulated data. The patterns obtained using the iterative clustering were found to be superior to those obtained using existing clustering algorithms.
Keywords: Clustering, microarray experiment, temporal pattern of gene expression data.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1252
8015 Sprayer Boom Active Suspension Using Intelligent Active Force Control
Authors: M. Tahmasebi, R.A. Rahman, M. Mailah, M. Gohari
The control of sprayer boom undesired vibrations pose a great challenge to investigators due to various disturbances and conditions. Sprayer boom movements lead to reduce of spread efficiency and crop yield. This paper describes the design of a novel control method for an active suspension system applying proportional-integral-derivative (PID) controller with an active force control (AFC) scheme integration of an iterative learning algorithm employed to a sprayer boom. The iterative learning as an intelligent method is principally used as a method to calculate the best value of the estimated inertia of the sprayer boom needed for the AFC loop. Results show that the proposed AFC-based scheme performs much better than the standard PID control technique. Also, this shows that the system is more robust and accurate.
Keywords: Active force control, sprayer boom, active suspension, iterative learning.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2164
8014 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
8013 Surface Flattening based on Linear-Elastic Finite Element Method
Authors: Wen-liang Chen, Peng Wei, Yidong Bao
This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.
Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3025
8012 Semiconvergence of Alternating Iterative Methods for Singular Linear Systems
Authors: Jing Wu
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 1443
8011 A New Derivative-Free Quasi-Secant Algorithm For Solving Non-Linear Equations
Authors: F. Soleymani, M. Sharifi
Abstract:Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.
Keywords: Non-linear equation, iterative methods, derivative-free, convergence.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1660