**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1731

# Search results for: iterative algorithms.

##### 1731 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.

##### 1730 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.

##### 1729 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.

##### 1728 The Riemann Barycenter Computation and Means of Several Matrices

**Authors:**
Miklos Palfia

**Abstract:**

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.

##### 1727 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

##### 1726 Iterative Solutions to Some Linear Matrix Equations

**Authors:**
Jiashang Jiang,
Hao Liu,
Yongxin Yuan

**Abstract:**

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.

##### 1725 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.

##### 1724 Iterative Clustering Algorithm for Analyzing Temporal Patterns of Gene Expression

**Authors:**
Seo Young Kim,
Jae Won Lee,
Jong Sung Bae

**Abstract:**

**Keywords:**
Clustering,
microarray experiment,
temporal
pattern of gene expression data.

##### 1723 Transportation Under the Threat of Influenza

**Authors:**
Yujun Zheng,
Qin Song,
Haihe Shi,
and Jinyun Xue

**Abstract:**

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

##### 1722 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.

##### 1721 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.

##### 1720 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.

##### 1719 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.

##### 1718 Computing the Loop Bound in Iterative Data Flow Graphs Using Natural Token Flow

**Authors:**
Ali Shatnawi

**Abstract:**

**Keywords:**
Data flow graph,
Iteration period bound,
Rateoptimalscheduling,
Recursive DSP algorithms.

##### 1717 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.

##### 1716 An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem

**Authors:**
Y. Wang

**Abstract:**

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is *O*(*CN*_{max}*n*^{2}) where *C* is the iterations, *N*_{max} is the maximum number of frequency quadrilaterals containing each edge and *n* is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5*n* edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

**Keywords:**
Frequency quadrilateral,
iterative algorithm,
sparse graph,
traveling salesman problem.

##### 1715 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.

##### 1714 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

##### 1713 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.

##### 1712 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.

##### 1711 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.

##### 1710 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.

##### 1709 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.

##### 1708 An Efficient Iterative Updating Method for Damped Structural Systems

**Authors:**
Jiashang Jiang

**Abstract:**

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.

##### 1707 Experimental Results about the Dynamics of the Generalized Belief Propagation Used on LDPC Codes

**Authors:**
Jean-Christophe Sibel,
Sylvain Reynal,
David Declercq

**Abstract:**

In the context of channel coding, the Generalized Belief Propagation (GBP) is an iterative algorithm used to recover the transmission bits sent through a noisy channel. To ensure a reliable transmission, we apply a map on the bits, that is called a code. This code induces artificial correlations between the bits to send, and it can be modeled by a graph whose nodes are the bits and the edges are the correlations. This graph, called Tanner graph, is used for most of the decoding algorithms like Belief Propagation or Gallager-B. The GBP is based on a non unic transformation of the Tanner graph into a so called region-graph. A clear advantage of the GBP over the other algorithms is the freedom in the construction of this graph. In this article, we explain a particular construction for specific graph topologies that involves relevant performance of the GBP. Moreover, we investigate the behavior of the GBP considered as a dynamic system in order to understand the way it evolves in terms of the time and in terms of the noise power of the channel. To this end we make use of classical measures and we introduce a new measure called the hyperspheres method that enables to know the size of the attractors.

**Keywords:**
iterative decoder,
LDPC,
region-graph,
chaos.

##### 1706 Determination of Sequential Best Replies in N-player Games by Genetic Algorithms

**Authors:**
Mattheos K. Protopapas,
Elias B. Kosmatopoulos

**Abstract:**

An iterative algorithm is proposed and tested in Cournot Game models, which is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player-s best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with “local NE traps"[14], where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.

**Keywords:**
Best response,
Cournot oligopoly,
genetic algorithms,
Nash equilibrium.

##### 1705 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.

##### 1704 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.

##### 1703 Some New Upper Bounds for the Spectral Radius of Iterative Matrices

**Authors:**
Guangbin Wang,
Xue Li,
Fuping Tan

**Abstract:**

**Keywords:**
doubly α diagonally dominant matrix,
eigenvalue,
iterative matrix,
spectral radius,
upper bound.

##### 1702 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.