Search results for: iterative improvement
1561 Approximating Fixed Points by a Two-Step Iterative Algorithm
Authors: Safeer Hussain Khan
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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 20121560 Transportation Under the Threat of Influenza
Authors: Yujun Zheng, Qin Song, Haihe Shi, and Jinyun Xue
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There are a number of different cars for transferring hundreds of close contacts of swine influenza patients to hospital, and we need to carefully assign the passengers to those cars in order to minimize the risk of influenza spreading during transportation. The paper presents an approach to straightforward obtain the optimal solution of the relaxed problems, and develops two iterative improvement algorithms to effectively tackle the general problem.
Keywords: Influenza spread, discrete optimization, stationary point, iterative improvement
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11741559 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices
Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12941558 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices
Authors: Zhuan-de Wang, Hou-biao Li, Zhong-xi Gao
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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 17701557 New High Order Group Iterative Schemes in the Solution of Poisson Equation
Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali
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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.
Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16711556 A New Preconditioned AOR Method for Z-matrices
Authors: Guangbin Wang, Ning Zhang, Fuping Tan
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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 15431555 Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices
Authors: Li Jiang, Baoguang Tian
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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 11971554 Fixed Points of Contractive-Like Operators by a Faster Iterative Process
Authors: Safeer Hussain Khan
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In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves andgeneralizes corresponding results in the literature in two ways: iterativeprocess is faster, operators are more general. At the end, we indicatethat the results can also be proved with the iterative process witherror terms.
Keywords: Contractive-like operator, iterative process, fixed point, strong convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17031553 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
Authors: Xingping Sheng
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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 12511552 Iterative solutions to the linear matrix equation AXB + CXTD = E
Authors: Yongxin Yuan, Jiashang Jiang
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In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.Keywords: matrix equation, iterative algorithm, parameter estimation, minimum norm solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15451551 Iterative Methods for An Inverse Problem
Authors: Minghui Wang, Shanrui Hu
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An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.
Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14741550 Efficient Iterative Detection Technique in Wireless Communication System
Authors: Hwan-Jun Choi, Sung-Bok Choi, Hyoung-Kyu Song
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Recently, among the MIMO-OFDM detection techniques, a lot of papers suggested V-BLAST scheme which can achieve high data rate. Therefore, the signal detection of MIMO-OFDM system is important issue. In this paper, efficient iterative V-BLAST detection technique is proposed in wireless communication system. The proposed scheme adjusts the number of candidate symbol and iterative scheme based on channel state. According to the simulation result, the proposed scheme has better BER performance than conventional schemes and similar BER performance of the QRD-M with iterative scheme. Moreover complexity of proposed scheme has 50.6% less than complexity of QRD-M detection with iterative scheme. Therefore the proposed detection scheme can be efficiently used in wireless communication.
Keywords: MIMO-OFDM, V-BLAST, QR-decomposition, QRD-M, DFE, Iterative scheme, Channel condition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20481549 Iterative Methods for Computing the Weighted Minkowski Inverses of Matrices in Minkowski Space
Authors: Xiaoji Liu, Yonghui Qin
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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, A
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14111548 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems
Authors: Shengfeng Li, Rujing Wang
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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 18701547 The Riemann Barycenter Computation and Means of Several Matrices
Authors: Miklos Palfia
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An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.
Keywords: Means, matrix means, operator means, geometric mean, Riemannian center of mass.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17821546 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application
Authors: Minghui Wang
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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 14811545 Existence of Iterative Cauchy Fractional Differential Equation
Authors: Rabha W. Ibrahim
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Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.
Keywords: Fractional calculus, fractional differential equation, Cauchy equation, Riemann-Liouville fractional operators, Volterra integral equation, non-expansive mapping, iterative differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26761544 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's
Authors: J. Sulaiman, M. Othman, M. K. Hasan
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Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Keywords: MEG iteration, second-order finite difference, weighted parameter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16971543 An Iterative Method for Quaternionic Linear Equations
Authors: Bin Yu, Minghui Wang, Juntao Zhang
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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 17581542 An Efficient Iterative Updating Method for Damped Structural Systems
Authors: Jiashang Jiang
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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 20781541 Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi
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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 19191540 Some New Upper Bounds for the Spectral Radius of Iterative Matrices
Authors: Guangbin Wang, Xue Li, Fuping Tan
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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 13331539 Iterative Solutions to Some Linear Matrix Equations
Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan
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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 18481538 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 13431537 Semiconvergence of Alternating Iterative Methods for Singular Linear Systems
Authors: Jing Wu
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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 16461536 New Iterative Algorithm for Improving Depth Resolution in Ionic Analysis: Effect of Iterations Number
Authors: N. Dahraoui, M. Boulakroune, D. Benatia
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In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov- Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.
Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22151535 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation
Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali
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In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15171534 Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method
Authors: Sachin Bhalekar, Varsha Daftardar-Gejji
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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 23271533 Iterative Learning Control of Two Coupled Nonlinear Spherical Tanks
Authors: A. R. Tavakolpour-Saleh, A. R. Setoodeh, E. Ansari
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This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.Keywords: Iterative learning control, spherical tanks, nonlinear system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12391532 New Explicit Group Newton's Iterative Methods for the Solutions of Burger's Equation
Authors: Tan K. B., Norhashidah Hj. M. Ali
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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1589