**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**16

# Search results for: Convergence analysis

##### 16 A Transform Domain Function Controlled VSSLMS Algorithm for Sparse System Identification

**Authors:**
Cemil Turan,
Mohammad Shukri Salman

**Abstract:**

**Keywords:**
Adaptive Filtering,
sparse system identification,
TD-LMS algorithm,
VSSLMS algorithm

##### 15 A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function

**Authors:**
Meriem Bahij,
Ahmed Nafidi,
Boujemâa Achchab,
Sílvio M. A. Gama,
José A. O. Matos

**Abstract:**

**Keywords:**
Simulation,
diffusion process,
discrete sampling,
bi-parameters weibull density function,
likelihood
estimation method,
stochastic diffusion equation,
trends
functions

##### 14 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

##### 13 On Algebraic Structure of Improved Gauss-Seidel Iteration

**Authors:**
O. M. Bamigbola,
A. A. Ibrahim

**Abstract:**

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

**Keywords:**
Convergence,
Gauss-Seidel iteration,
algebraic structure,
Linear system of equations

##### 12 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations

##### 11 Convergence Analysis of an Alternative Gradient Algorithm for Non-Negative Matrix Factorization

**Authors:**
Chenxue Yang,
Mao Ye,
Zijian Liu,
Tao Li,
Jiao Bao

**Abstract:**

Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.

**Keywords:**
Stability,
Convergence,
equilibrium point,
Non-negative matrix factorizations,
cAG
algorithm

##### 10 On Convergence Property of MINRES Method for Solving a Complex Shifted Hermitian Linear System

**Authors:**
Guiding Gu,
Guo Liu

**Abstract:**

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

**Keywords:**
complex shifted linear system,
Hermitian matrix,
MINRES method

##### 9 On the Modeling and State Estimation for Dynamic Power System

**Authors:**
A. Thabet,
M. Boutayeb,
M. N. Abdelkrim

**Abstract:**

This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.

**Keywords:**
Power System,
extended Kalman filter,
convergence analysis,
Dynamic decoupled model,
Time computing

##### 8 Alternative Convergence Analysis for a Kind of Singularly Perturbed Boundary Value Problems

**Authors:**
Jiming Yang

**Abstract:**

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

**Keywords:**
green's function,
convergence analysis,
Moving mesh,
singularly perturbed,
equi-distribution

##### 7 Convergence Analysis of the Generalized Alternating Two-Stage Method

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

**Abstract:**

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

**Keywords:**
Convergence,
Linear System,
Generalized alternating two-stage method

##### 6 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

**Authors:**
Jalil Rashidinia,
Reza Jalilian

**Abstract:**

**Keywords:**
Convergence,
Quintic non-polynomial spline,
Boundary formula,
Obstacle problems

##### 5 An Expectation of the Rate of Inflation According to Inflation-Unemployment Interaction in Croatia

**Authors:**
Zdravka Aljinović,
Snježana Pivac,
Boško Šego

**Abstract:**

**Keywords:**
Unemployment,
Inflation,
Differencing,
time path

##### 4 On the Fast Convergence of DD-LMS DFE Using a Good Strategy Initialization

**Authors:**
Y.Ben Jemaa,
M.Jaidane

**Abstract:**

In wireless communication system, a Decision Feedback Equalizer (DFE) to cancel the intersymbol interference (ISI) is required. In this paper, an exact convergence analysis of the (DFE) adapted by the Least Mean Square (LMS) algorithm during the training phase is derived by taking into account the finite alphabet context of data transmission. This allows us to determine the shortest training sequence that allows to reach a given Mean Square Error (MSE). With the intention of avoiding the problem of ill-convergence, the paper proposes an initialization strategy for the blind decision directed (DD) algorithm. This then yields a semi-blind DFE with high speed and good convergence.

**Keywords:**
convergence speed,
Adaptive decision feedback equalizer,
PerformanceAnalysis,
Finite Alphabet Case,
Ill-Convergence

##### 3 Analysis of Blind Decision Feedback Equalizer Convergence: Interest of a Soft Decision

**Authors:**
S. Cherif,
S. Marcos,
M. Jaidane

**Abstract:**

**Keywords:**
convergence analysis,
Blind DFEs,
decision-directed algorithm,
constant
modulus algorithm,
cost function analysis,
soft
decision

##### 2 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

**Authors:**
Talaat S. El-Danaf

**Abstract:**

**Keywords:**
Quartic nonpolynomial spline,
Two-point boundary
value problem

##### 1 Convergence Analysis of a Prediction based Adaptive Equalizer for IIR Channels

**Authors:**
Miloje S. Radenkovic,
Tamal Bose

**Abstract:**

**Keywords:**
Adaptive Filtering,
convergence analysis,
Adaptive blind equalizer,
Recursive leastsquares