**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4181

# Search results for: Iterative Methods

##### 4181 Iterative Methods for An Inverse Problem

**Authors:**
Minghui Wang,
Shanrui Hu

**Abstract:**

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.

##### 4180 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems

**Authors:**
Shengfeng Li,
Rujing Wang

**Abstract:**

**Keywords:**
Iterative method,
Fixed-point iteration,
Thiele's continued
fraction,
Order of convergence.

##### 4179 Parallel Multisplitting Methods for Singular Linear Systems

**Authors:**
Guangbin Wang,
Fuping Tan

**Abstract:**

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.

##### 4178 Approximating Fixed Points by a Two-Step Iterative Algorithm

**Authors:**
Safeer Hussain Khan

**Abstract:**

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.

##### 4177 Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems

**Authors:**
Davod Khojasteh Salkuyeh,
Sayyed Hasan Azizi

**Abstract:**

**Keywords:**
rank deficient least squares problems,
AOR iterativemethod,
Gauss-Seidel iterative method,
semiconvergence.

##### 4176 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.

##### 4175 New Explicit Group Newton's Iterative Methods for the Solutions of Burger's Equation

**Authors:**
Tan K. B.,
Norhashidah Hj. M. Ali

**Abstract:**

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).

##### 4174 Adaptation of Iterative Methods to Solve Fuzzy Mathematical Programming Problems

**Authors:**
Ricardo C. Silva,
Luiza A. P. Cantao,
Akebo Yamakami

**Abstract:**

**Keywords:**
Fuzzy Theory,
Nonlinear Optimization,
Fuzzy Mathematics Programming.

##### 4173 New High Order Group Iterative Schemes in the Solution of Poisson Equation

**Authors:**
Sam Teek Ling,
Norhashidah Hj. Mohd. Ali

**Abstract:**

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.

##### 4172 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

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

**Abstract:**

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

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

##### 4171 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

**Authors:**
J. Sulaiman,
M. Othman,
M. K. Hasan

**Abstract:**

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.

##### 4170 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 4169 Optimal Relaxation Parameters for Obtaining Efficient Iterative Methods for the Solution of Electromagnetic Scattering Problems

**Authors:**
Nadaniela Egidi,
Pierluigi Maponi

**Abstract:**

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

**Keywords:**
Fredholm integral equation,
iterative method,
preconditioning,
scattering problem.

##### 4168 Two Iterative Algorithms to Compute the Bisymmetric Solution of the Matrix Equation A1X1B1 + A2X2B2 + ... + AlXlBl = C

**Authors:**
A.Tajaddini

**Abstract:**

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

**Keywords:**
Bisymmetric matrices,
Paige’s algorithms,
Least
square.

##### 4167 Iterative Methods for Computing the Weighted Minkowski Inverses of Matrices in Minkowski Space

**Authors:**
Xiaoji Liu,
Yonghui Qin

**Abstract:**

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

##### 4166 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

**Authors:**
Minghui Wang

**Abstract:**

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.

##### 4165 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation

**Authors:**
Kew Lee Ming,
Norhashidah Hj. Mohd. Ali

**Abstract:**

**Keywords:**
Telegraph equation,
explicit group iterative scheme,
domain decomposition algorithm,
parallelization.

##### 4164 On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
H. N. Ude

**Abstract:**

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

**Keywords:**
conjugate gradient,
linear equations,
symmetric and positive definite matrix,
Gauss-Seidel,
Jacobi,
algorithm

##### 4163 Numerical Study of Iterative Methods for the Solution of the Dirichlet-Neumann Map for Linear Elliptic PDEs on Regular Polygon Domains

**Authors:**
A. G. Sifalakis,
E. P. Papadopoulou,
Y. G. Saridakis

**Abstract:**

**Keywords:**
Elliptic PDEs,
Dirichlet to Neumann Map,
Global Relation,
Collocation,
Iterative Methods,
Jacobi,
Gauss-Seidel,
GMRES,
Bi-CGSTAB.

##### 4162 Jacobi-Based Methods in Solving Fuzzy Linear Systems

**Authors:**
Lazim Abdullah,
Nurhakimah Ab. Rahman

**Abstract:**

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

**Keywords:**
Fuzzy linear systems,
Jacobi,
Jacobi Over-
Relaxation,
Refinement of Jacobi,
Refinement of Jacobi Over-
Relaxation.

##### 4161 A New Preconditioned AOR Method for Z-matrices

**Authors:**
Guangbin Wang,
Ning Zhang,
Fuping Tan

**Abstract:**

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.

##### 4160 Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices

**Authors:**
Li Jiang,
Baoguang Tian

**Abstract:**

**Keywords:**
Z-matrix,
mixed-type splitting iterative method,
precondition,
comparison theorem,
linear system.

##### 4159 Fixed Points of Contractive-Like Operators by a Faster Iterative Process

**Authors:**
Safeer Hussain Khan

**Abstract:**

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.

##### 4158 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 4157 Iterative solutions to the linear matrix equation AXB + CXTD = E

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
matrix equation,
iterative algorithm,
parameter estimation,
minimum norm solution.

##### 4156 Efficient Iterative Detection Technique in Wireless Communication System

**Authors:**
Hwan-Jun Choi,
Sung-Bok Choi,
Hyoung-Kyu Song

**Abstract:**

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.

##### 4155 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

**Authors:**
Osama Yusuf Ababneh

**Abstract:**

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.

##### 4154 Existence of Iterative Cauchy Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

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.

##### 4153 An Iterative Method for Quaternionic Linear Equations

**Authors:**
Bin Yu,
Minghui Wang,
Juntao Zhang

**Abstract:**

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.

##### 4152 Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations

**Authors:**
Rafat Alshorman,
Safwan Al-Shara',
I. Obeidat

**Abstract:**

**Keywords:**
Nonlinear Algebraic Equations,
Iterative Methods,
Homotopy
Analysis Method.