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In this paper, Coupled Fractional Reduced Differential Transform method (CFRDTM) is applied to solve timefractional Drinfeld-Sokolov-Wilson system. In the procedure of the method, we can obtain the solutions which take the form of convergent series. This paper will present a comparison between the solutions obtained by CFRDTM and the previously known results using the residual power series method. The comparison demonstrates that both of the methods are efficient and easily implemented for getting approximate solutions of time-fractional Drinfeld-Sokolov-Wilson system. Furthermore, it also indicates that the results in previous literature contain errors. [ABSTRACT FROM AUTHOR]

Firefly algorithm is an effective and global searching algorithm which has been widely used in a lot of areas successfully. This paper proposes an improved firefly algorithm that is called DFA algorithm and focuses on the application of DFA to the portfolio optimization problem. The experimental results show that DFA algorithm is more efficient than genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and firefly algorithm, and it has higher convergence precision and faster convergence speed. [ABSTRACT FROM AUTHOR]

In this paper, we present a new preconditioner which generalizes two known preconditioners proposed by Wang et al. (2009) and A. J. Li (2011), and prove that the convergence rate of the AOR method with the new preconditioner is faster than the preconditioners introduced by Wang et al. Moreover, we propose other two new preconditioners and study the convergence rates of the new preconditioned AOR methods for solving linear systems. Comparison results show that the new preconditioned AOR methods are better than those of the preconditioned AOR methods presented by J. H. Yun (2011) and A. J. Li (2012). Finally, numerical experiments are provided to confirm the theoretical results studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a new preconditioner which generalizes two known preconditioners proposed by Wang et al. (2009) and A. J. Li (2011), and prove that the convergence rate of the AOR method with the new preconditioner is faster than the preconditioners introduced by Wang et al. Moreover, we propose other two new preconditioners and study the convergence rates of the new preconditioned AOR methods for solving linear systems. Comparison results show that the new preconditioned AOR methods are better than those of the preconditioned AOR methods presented by J. H. Yun (2011) and A. J. Li (2012). Finally, numerical experiments are provided to confirm the theoretical results studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we suppose and analyze a differential quadrature method for the numerical solution of fractional Logistic differential equation. The fractional derivative is described in the Caputo sense. Explicit expressions of weighting coefficients for approximation of fractional derivatives are derived and are utilized to reduce the Logistic differential equation to system of algebraic equations. The convergence order of the proposed method is investigated in the infinity norm. Numerical examples are presented to verify the efficiency and accuracy of the proposed method. The results reveal that the method is accurate and easy to implement. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new regularized Fourier series, that is the Gauss-regularized Fourier series. Moreover, we find this regularized Fourier series can be used to compute the Fourier transforms of bandlimited signals. When the regularization parameter tends to zero, we prove that this regularized Fourier series is uniform and L²-convergence. Numerical results demonstrate the superiority of the new method over some previous methods. [ABSTRACT FROM AUTHOR]

In this paper, a Dirichlet-Neumann alternating method using elliptical arc artificial boundary is designed to solve exterior Poisson problem with a concave angle. It is shown that the method is equivalent to a preconditioned Richardson iteration. The convergence of this method and its discretization are studied. Finally, some numerical examples are given to show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, we propose the fourth stage of the inverse polynomial scheme for the numerical solution of initial value problems of ordinary differential equations. Binomial expansion and Taylor's series method are used towards the derivation of the scheme. We further study the analysis properties to show the efficiency of the method. Numerical experiments are carried out and the results are compared with the theoretical solution and some existing methods to show that it is adequate, effective and computationally time friendly. [ABSTRACT FROM AUTHOR]

A new Taylor-series method which was originally developed for the solution of one-dimensional integral equations is extended to solve multivariate nonlinear integral equations. In this paper, a new method is constructed to approximate the solutions of a class of multivariate Hammerstein equations. One of the strength of the new method is that it lends itself to parallel computation. Hence it is a very highly efficient method. Another strength of the proposed method is that it also gives highly accurate approximations for all the derivatives of the solution up to the order of the Taylor-series approximation used in the method. Numerical examples are given to illustrate the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

In this paper, we first provide semi-convergence analysis for a special GPIU(Generalized Parameterized Inexact Uzawa) method with singular preconditioners for solving singular saddle point problems. We next provide a methodology of how to choose nearly quasi-optimal parameters of the special GPIU method. Lastly, numerical experiments are carried out to examine the effectiveness of the special GPIU method with singular preconditioners by comparing its performance with that of other existing iterative methods for solving singular saddle point problems. [ABSTRACT FROM AUTHOR]

For globally solving sum of linear ratios problem (SLRP), this paper presents a new branch-and-bound method. In this method, a new linear relaxation technique is proposed firstly; then, the initial problem SLRP is solved by a sequence of linear programming problems. Meanwhile, to improve the convergence speed of our algorithm, two accelerating techniques are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a highly accurate parallel difference scheme for the fourth-order diffusion equation is studied. Based on a group of new Saul'yev type asymmetric difference schemes, a high-order, unconditionally stable and parallel alternating group explicit scheme is derived. The scheme is fourth-order truncation error in space, which is much more accurate than the known methods. Numerical experiments are performed to examine the convergence, unconditional stability and accuracy. A comparison of the accuracy of this scheme with the prior AGE methods is presented. [ABSTRACT FROM AUTHOR]

Aiming at typical shortcomings including large memory occupation of GA(Genetic Algorithm) in evolvable hardware and poor searching capabilities of CGA(Compact Genetic Algorithm) in solving complex problems, this paper presents an improved compact genetic algorithm named ne-TCGA(none-persistent elitism Compact Genetic Algorithm with Tendency). This algorithm is combined with the analysis of convergent trend on the basis of TCGA (Compact Genetic Algorithm with Tendency) and it adopts the strategy of temporary elitist preservation, which both ensure the adequate selection pressure, and maintains the diversity of the population in the evolutionary process. According to the experiment, it can be concluded that the ne-TCGA applied in evolvable hardware has better computational efficiency than other random search algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes neural network for computing the eigenvectors of Hermitian matrices. For the eigenvalues of Hermitian matrices, we establish an explicit representation for the solution of the neural network based on Hermitian matrices and analyze its convergence property. We also consider to compute the eigenvectors of skew-symmetric matrices and skew-Hermitian matrices, corresponding to the imaginary maximal or imaginary minimal eigenvalue, based on the neural network for computing the eigenvectors of Hermitian matrices. Numerical examples are given to illustrate our theoretical result are valid. [ABSTRACT FROM AUTHOR]

In this paper, for solving generalized linear fractional programming (GLFP), a new branch-and-reduce approach is presented. Firstly, an equivalent problem (EP) of GLFP is given; then, a new linear relaxation technique is proposed; finally, the problem EP is reduced to a sequence of linear programming problems by using the new linear relaxation technique. Meanwhile, to improve the convergence speed of our algorithm, two reducing techniques are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we reformulate the stochastic generalized second-order cone complementarity problems as boxconstrained optimization problems. If satisfy the condition that the reformulation's objective value is zero, the solutions of box-constrained optimization problems are also solutions of stochastic generalized second-order cone complementarity problems. Since the box-constrained minimization problems contain an expectation function, we then employ sample average approximation method to give approximation problems of the box-constrained minimization reformulation. Meanwhile the convergence results of global solutions and stationary points for the corresponding approximation problems are considered. [ABSTRACT FROM AUTHOR]

In this paper, an iteration method using elliptical arc artificial boundary is designed to solve exterior Poisson problem with a concave angle. It is shown that the iteration method is equivalent to a Schwarz alternating method. The convergence of this method is given. The convergence rate is analyzed in details for a typical domain. Finally, some numerical examples are given, which show the effectiveness of the iteration method. [ABSTRACT FROM AUTHOR]

In this paper, we present a finite difference scheme for a class of time fractional diffusion equation with variable coefficient, where the fractional derivative is defined by the Caputo derivative. The present algorithm is unconditionally stable, and possess spatial sixth order and temporal 2 -α order accuracy, which is an improvement of the spatial fourth order accuracy in the existing results. Theoretical analysis including local truncating error, unique solvability, stability and convergence for this algorithm is fulfilled. Then based on this finite difference scheme, we also investigate the construction of unconditionally stable finite difference scheme for a class of time fractional parabolic equation with spatial fourth derivative. In order to testify the efficiency of the algorithms as well as the convergence orders, some numerical examples are presented. [ABSTRACT FROM AUTHOR]

Accurate short-term traffic forecasting can relieve traffic congestion and improve the mobility of transportation, which is very important for management modernization of transportation systems. However, it is quite difficult to predict effectively and accurately short-term traffic information since traffic information shows the strongly nonlinear, complex and uncertain characteristics. In this paper, a new hybrid model based on grey neural network and fruit fly optimization algorithm (FOA) is proposed to solve this problem. The FOA is used to select the appropriate parameter values of the grey neural network model, thereby improving the accuracy of forecasting model. The proposed hybrid model can exploit sufficiently the characteristics of grey system model requiring less data, the non-linear map of neural networks and the quick-speed convergence of FOA, and has simpler structure. The effectiveness of this proposed hybrid model is proved by experiment simulation. The experiment results show that the proposed model has better performance than the single grey model GM(1,1), the single back-propagation neural network (BPNN) model, the combined model of them, i.e., the grey neural network (GNN) model, and the GNN model with particle swarm optimization (GNN-PSO), on short-term traffic forecasting. [ABSTRACT FROM AUTHOR]

In this paper, we study the fuzzy differential equations in the quotient space of fuzzy numbers. We deal with the convergence of successive approximations of the initial value problem of the fuzzy differential equations under the general uniqueness assumption of Perron type utilizing the comparison functions that is rather instructive. We also discuss the approximate solutions and the error estimates between the solutions and approximate solutions. [ABSTRACT FROM AUTHOR]

The most important feature of numerical methods based on a spectral decomposition is the best convergence rate (even infinite for infinitely regular functions) with respect to all other methods used in dealing with the solution to most of the differential equations. However this is true under the mandatory condition that at each time step of the evolving numerical solution no discontinuity occurs, either advected from the initial condition or self-generated (shock wave) by the non-linearity of the problem. In the first part of this paper we will point out that also by using any second or higher order pseudo-spectral method applied to the linear advection equation, one can experience the appearance in the numerical solution of the celebrated Gibbs phenomenon, located at the discontinuity points of the initial condition. As matter of fact in order to avoid such a drawback, the only applicable methods are the first order ones. In particular for stability reasons, we chose to consider the implicit Euler method and experienced that, even the Richardson's extrapolation is not able in increasing the accuracy without falling into the same problem. As a partial remedy, we propose a novel way to improve the accuracy of the implicit Euler first order pseudo-spectral method by reducing the coefficient of its truncation error leading term via a time one-step extrapolation-like technique. The second part of the paper is instead devoted to show how for dispersive differential problems the use of pseudo-spectral methods represents a very powerful numerical approach in finding out the notorious solitons dynamics. In particular we will deal with the celebrated KdV equation in 1D and its generalization in 2D. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convergence of a new finite steps iterative sequence with mean errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and generalize some results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified regularized Newton method (M-RNM) for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses local quadratic convergence under a local error bound condition. A globally convergent M-RNM algorithm is also given by using trust region technique. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to discuss the convergence of uncertain variables and the truncation method for uncertain measure. Based on uncertain measure theory, we propose the concepts of convergence with uncertain measure 1 and convergence almost everywhere. Then we investigate some properties of the convergence concepts. Finally, we present and prove the truncation method in uncertain environment. All obtained results are the natural extensions of the classical conclusions to the case where the measure tool is non-additive. [ABSTRACT FROM AUTHOR]

In this paper, a compact finite difference method to solve the Rosenau-RLW equation is proposed. A numerical tool is applied to the model by using a three-level average implicit finite difference technique. The fundamental conservative property of the equation is preserved by the presented numerical scheme, and the existence and uniqueness of the numerical solution are proved. Moreover, the convergence and stability of the numerical solution are also shown. The new method gives second- and fourth-order accuracy in time and space, respectively. The algorithm uses five-point stencil to approximate the derivatives for the space discretization. The numerical experiments show that the proposed method improves the accuracy of the solution significantly. [ABSTRACT FROM AUTHOR]

In this paper, three preconditioned parallel multisplitting methods are established for solving the large sparse linear systems, including local preconditioned parallel multisplitting relaxation method, global preconditioned parallel multisplitting relaxation method and global preconditioned nonstationary parallel multisplitting relaxation method. The convergence and comparison results of the methods associated with USAOR multisplitting are given when the coefficient matrices of the linear systems are H-matrices. We prove three preconditioned parallel multisplitting USAOR method are better than parallel multisplitting USAOR methods for M-matrices linear systems. Finally, numerical examples are given to illustrate the methods are valid. [ABSTRACT FROM AUTHOR]

In recent years, progress has been made in the analysis of global convergence of clonal selection algorithms (CSA), but most analyses are based on the theory of Markov chain, which depend on the description of the transition matrix and eigenvalues. However, such analyses are very complicated, especially when the population size is large, and are presented for particular implementations of CSA. In this paper, instead of the traditional Markov chain theory, we introduce martingale theory to prove the convergence of a class of CSA, called elitist clonal selection algorithm (ECSA). Using the submartingale convergence theorem, the best individual affinity evolutionary sequence is described as a submartingale, and the almost everywhere convergence of ECSA is derived. Particularly, the algorithm is proved convergent with probability 1 in finite steps when the state space of population is finite. This new proof of global convergence analysis of ECSA is more simplified and effective, and not implementation specific. [ABSTRACT FROM AUTHOR]

A one-step implicit hybrid block solution method for initial value problems of general second order ordinary differential equations has been studied in this paper. The one-step method is augmented by the inclusion of off step points to enable the multistep procedure. This guaranteed zero stability as well as consistency of the resulting method. The convergence and weak stability properties of the new method have been established. Results from the new method compared with those obtained from existing methods show that the new method gives better accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we consider, a finite dimensional realization of Newton type iterative method for Lavrentiev regularization of ill-posed equations. Precisely we consider the ill-posed equation F(x) = f when the available data is fδ with ||f - fδ|| ≤ δ and the operator F : D(F) ⊆ X → X is a nonlinear monotone operator defined on a real Hilbert space X. The error estimate obtained under a general source condition on x0 - x̂ (where x0 is the initial guess and x̂ is the solution of F(x) = f) is of optimal order. The regularization parameter α is chosen according to the adaptive method considered by Perverzev and Schock (2005). An example is provided to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A new approach to generalize Principal Components Analysis in order to handle nonlinear structures has been recently proposed by the authors: quasi-linear PCA (qlPCA). It includes spline transformation of the original variables and the qualifier quasi was chosen to emphasize the exclusive use of linear splines. Alternating least squares fitting of a suitable objective loss function is the mechanism for achieving spline optimal transformation and nonlinear principal components. Optimal transformations are explicitly known after convergence and allow a straightforward projection of new observations onto the nonlinear principal components space as well as reconstruction the original variables. QlPCA reports model summary in a linear PCA fashion and allows the introduction of the piecewise loadings concept. This paper provides further details on qlPCA and its properties. Results of a simulation study are also presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with Monte Carlo simulation of generalized Asian option prices where the underlying asset is modeled by a geometric (finite-activity) Lévy process. A control variate technique is proposed to improve standard Monte Carlo method. Some convergence results for plain Monte Carlo simulation of generalized Asian options are proven, and a detailed numerical study is provided showing the performance of the variance reduction compared to straightforward Monte Carlo method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm M-SMFTF for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. The computational complexity was reduced from 7L to 6L, where L is the finite impulse response filter length. Furthermore, this computational complexity can be significantly reduced to (2L+4P) when used with a reduced P-size forward predictor. This algorithm presents a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal. The proposed algorithm outperforms the classical adaptive algorithms because of its convergence speed which approaches that of the RLS algorithm and its computational complexity which is slightly greater than the one of the normalized LMS algorithm. [ABSTRACT FROM AUTHOR]

Nonlinear inter-symbol interference leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel recurrent interval type-2 fuzzy neural network with asymmetric membership functions (RT2FNN-A) is proposed for nonlinear channel equalization. The RT2FNN-A uses the interval asymmetric type-2 fuzzy sets and it implements the fuzzy logic system in a five-layer neural network structure. The RT2FNN-A is an extensive results of type-2 fuzzy neural network to provide memory elements for capturing the system's dynamic information and has the properties of high approximation accuracy and small network structure. Based on the Lyapunov theorem and gradient descent method, the convergence of RT2FNN-A is guaranteed and the corresponding learning algorithm is derived. In addition, the RT2FNN-A is applied in the nonlinear channel equalization to show the performance and effectiveness of RT2FNN-A system. [ABSTRACT FROM AUTHOR]

In this paper we discuss preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for direct solvers and ILU pre-conditioners is introduced that improves the convergence of the solvers. We compare Bi-CGSTAB and a newly developed Krylov subspace method IDR(s) preconditioned with ILU. Both 2D and 3D experiments are used to measure the performance of the preconditioners. [ABSTRACT FROM AUTHOR]

In this paper, we construct Ishikawa iterative scheme with errors for nonself nonexpansive maps and approximate fixed points of these maps through weak and strong convergenc of the scheme. [ABSTRACT FROM AUTHOR]