**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**9

# iterative algorithm Related Publications

##### 9 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:**
traveling salesman problem,
iterative algorithm,
frequency quadrilateral,
sparse graph

##### 8 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,
Optimal approximation,
damped structural
system

##### 7 Effect of Iterative Algorithm on the Performance of MC-CDMA System with Nonlinear Models of HPA

**Authors:**
R. Blicha

**Abstract:**

High Peak to Average Power Ratio (PAPR) of the transmitted signal is a serious problem in multicarrier systems (MC), such as Orthogonal Frequency Division Multiplexing (OFDM), or in Multi-Carrier Code Division Multiple Access (MC-CDMA) systems, due to large number of subcarriers. This effect is possible reduce with some PAPR reduction techniques. Spreading sequences at the presence of Saleh and Rapp models of high power amplifier (HPA) have big influence on the behavior of system. In this paper we investigate the bit-error-rate (BER) performance of MC-CDMA systems. Basically we can see from simulations that the MC-CDMA system with Iterative algorithm can be providing significantly better results than the MC-CDMA system. The results of our analyses are verified via simulation.

**Keywords:**
BER,
iterative algorithm,
MC-CDMA,
PAPR,
Saleh,
Rapp,
Spreading Sequences

##### 6 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:**
Fixed Point,
contractive-like operator,
strong convergence,
iterative algorithm

##### 5 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:**
iterative algorithm,
Real representation,
Quaternionic linear equations

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

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

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

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

**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:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

##### 2 An Iterative Updating Method for Damped Gyroscopic Systems

**Authors:**
Yongxin Yuan

**Abstract:**

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

**Keywords:**
Model Updating,
iterative algorithm,
Optimal approximation,
gyroscopic system,
partially prescribed spectral data

##### 1 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:**
iterative algorithm,
Matrix Equation,
bisymmetric matrix,
least squares problem,
like-minimum norm