Search

The purpose of this paper is to introduce a new mapping for a finite family of accretive operators and introduce an iterative algorithm for finding a common zero of a finite family of accretive operators in a real reflexive strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function invariant on [0, ∞). Furthermore, we prove the strong convergence under some certain conditions. The results obtained in this paper improve and extend the corresponding ones announced by many others. [ABSTRACT FROM AUTHOR]

A novel localization algorithm, which considers nonline-of-sight (NLOS) propagation, is proposed in this paper. By introducing a transfer function that relates the field at a given receiver to the source as a function of frequency and position, the NLOS effect can be mitigated and the propagation channel can be calibrated back to free space. The simulation results demonstrate that the proposed algorithm performs much better than that using the usual line-of-sight time difference of arrival (TDOA) localization, and the accuracy is only limited by the sampling frequency. The measurements verify the improvement in using the improved TDOA method versus the usual TDOA method. [ABSTRACT FROM AUTHOR]

Solving equations of the form H ( x ) = 0 is usually done by applying iterative methods. The main interest of this paper is to improve the domain of starting points for Steffensen’s method. In general, the accessibility of iterative methods that use divided differences in their algorithms is reduced, since there are difficulties in the choice of starting points to guarantee the convergence of the methods. In particular, by using a decomposition of the operator H and applying a special type of iterative methods, which combine two iterative schemes in the algorithms, we can improve the accessibility of Steffensen’s method. Moreover, we analyze the local convergence of the new iterative method proposed in two cases: when H is differentiable and H is non-differentiable. The dynamical properties show that the method also improves the region of accessibility of Steffensen’s method for non-differentiable operators. So, we present an alternative for the non-applicability of Newton’s method to non-differentiable operators that improves the accessibility of Steffensen’s method. The theoretical results are illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

We previously introduced a new efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. The new 2-D efficient algorithm is based on the use of an iterative procedure to reduce the splitting error associated with the perturbation term, and it does not involve any nonphysical intermediate variables. Numerical results indicated that the new efficient algorithm shows better performance for modeling some regions with larger spatial derivatives of the field. In this paper, we extend this approach to a full 3-D wave. Numerical formulations of the new 3-D Laguerre-based FDTD method are devised and simulation results are compared to those using the conventional 3-D FDTD method and the alternating-direction implicit (ADI) FDTD method. We numerically verify that, at the comparable accuracy, the efficiency of the proposed method with an iterative procedure is superior to the FDTD method and the ADI -FDTD method. Also, in order to verify the stability of the iterative procedure, we present a convergence analysis and a long-time simulation to it in the paper. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources. [ABSTRACT FROM AUTHOR]

This paper presents an iterative algorithm for G 2 multiwise merging of Bézier curves. By using the G 2 constraint, the L 2 distance is represented after simplification as a quartic polynomial in two parameters relating to the magnitudes of end tangents of the merged curve. These two parameters are restricted in a feasible region, in order for the merged curve to preserve the specified directions of end tangents. Then G 2 multiwise merging is formulated as a constrained minimization problem, and the classic projected Newton method is applied to find the minimizer. Some extensions of multiwise merging using G 3 constraints, other energy functionals and curve representations are also outlined. Several comparative examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic systems described by the autoregressive output error autoregressive (AR-OEAR) models. The AR-OEAR model is a special output error model which has an extra autoregressive term of the output signal. Basing on the auxiliary model idea, the recursive method and the iterative principle, the auxiliary model based recursive and iterative least squares algorithms are proposed to estimate the parameters of the autoregressive output error autoregressive system which contains the autoregressive output error system model and the autoregressive noise model, respectively. The simulation results indicate that the proposed algorithms can work well. [ABSTRACT FROM AUTHOR]

For finding a common solution of generalized equilibrium problem, fixed point problem and the zero points of the sum of two operators, a regularization algorithm is established in the framework of real Hilbert spaces. And the strong convergence theorem is obtained under certain assumptions. The main results presented in this paper are useful in nonlinear analysis and optimization. Moreover, the results and corollaries extend the corresponding conclusions proposed by many authors. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a split hierarchical monotone variational inclusion problem (SHMVIP) which includes split variational inequality problems, split monotone variational inclusion problems, split hierarchical variational inequality problems, etc., as special cases. An iterative algorithm is proposed to compute the approximate solutions of an SHMVIP. The weak convergence of the sequence generated by the proposed algorithm is studied. We present an example to illustrate our algorithm and convergence result. [ABSTRACT FROM AUTHOR]

In the present paper, we propose an iterative algorithm for solving the generalized (P, Q)-reexive solution of the quaternion matrix equation Σul=1 AlXBl + Σvs=1 CsX̃Ds = F. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over a generalized (P, Q)-reexive matrix X, a generalized (P, Q)-reexive solution can be obtained within finite iteration steps in the absence of roundoff errors, and the least Frobenius norm generalized (P, Q)-reexive solution can be obtained by choosing an appropriate initial iterative matrix. Furthermore, the optimal approximate generalized (P, Q)-reexive solution to a given matrix X0 can be derived by finding the least Frobenius norm generalized (P, Q)-reexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of solving the general coupled matrix equations (including several linear matrix equations as special cases) which plays important roles in system and control theory. Based on the conjugate gradients squared (CGS) method, a simple and efficient matrix algorithm is derived to solve the general coupled matrix equations. The derived iterative algorithm is illustrated by two numerical examples and is compared with other popular iterative solvers in use today. [Copyright &y& Elsevier]

Abstract: In this paper, we present an iterative algorithm for computing the largest singular value of a nonnegative rectangular tensor. We establish the convergence of this algorithm for any irreducible nonnegative rectangular tensor. [Copyright &y& Elsevier]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on identification problems for Hammerstein systems with saturation and dead-zone nonlinearities. An appropriate switching function is introduced to derive an identification model with fewer parameters and all the unknown parameters can be estimated by using an iterative method. A numerical simulation is carried out to show the effectiveness of the proposed method. [Copyright &y& Elsevier]

In this paper, a new dc offset removal algorithm for real-time simulations is proposed. Physically transferred signals in a real-time simulation interface tend to contain a dc offset component for various reasons. This component decreases the accuracy and stability of real-time simulations. The dc offset tends to change according to circumstances which include changes in the system configuration and effects of the external environment which makes the static dc offset removal scheme inefficient. The proposed algorithm can estimate and remove a dc offset component dynamically from the input signal of the hardware under test. In the proposed algorithm, the optimal constant for the condition equation is calculated by using an iterative method and is used to estimate the frequency, time, magnitude, and dc offset component of the input signal. Four sampling points are used to calculate the optimal constant in each step. The proposed algorithm has relatively fast speed and good accuracy in comparison to conventional dc offset removal algorithms. In order to verify the performances of the proposed algorithm, offline and real-time dc offset estimation simulation tests were performed. The results of the simulation tests showed that the proposed algorithm can estimate the dc offset component promptly and exactly and can be applied to real-time simulations. [ABSTRACT FROM AUTHOR]

Abstract: An matrix is said to be -symmetric if for all , where is given. In this paper, by extending the idea of the conjugate gradient least squares (CGLS) method, we construct an iterative method for solving a generalized inverse eigenvalue problem: minimizing where is the Frobenius norm, and are given, and is a -symmetric matrix to be solved. Our algorithm produces a suitable such that within finite iteration steps in the absence of roundoff errors, if such an exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor. We prove this method converges for any irreducible nonnegative tensor. We also apply this method to study the positive definiteness of a multivariate form. [Copyright &y& Elsevier]

Thermal asperities (TAs) cause a crucial problem in magnetic recording systems because they can cause a burst of errors in data detection process. Without a TA detection and correction algorithm, the system performance can be unacceptable, depending on how severe the TA effect is. This paper proposes an iterative scheme to suppress the TA effect. This scheme jointly performs TA suppression and turbo equalization on the partial-response channels with error-correction codes. At each turbo iteration, an improved readback signal is obtained by subtracting the reconstructed TA signal from the TA-affected readback signal, where the reconstructed TA signal is computed based on a least-squares fitting technique with an aid of soft decisions from previous turbo iterations. Simulation results indicate that the proposed scheme outperforms the conventional receiver with separate TA suppression and turbo equalization, and is only marginally more complex than the conventional receiver. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear iteration method for solving a class of two-dimensional nonlinear coupled systems of parabolic and hyperbolic equations is studied. A simple iterative finite difference scheme is designed; the calculation complexity is reduced by decoupling the nonlinear system, and the precision is assured by timely evaluation updating. A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme. The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution. The corresponding nonlinear FIFD scheme is stable and gives the same order of approximation. Numerical tests verify the results of the theoretical analysis. The discrete functional analysis and inductive hypothesis reasoning techniques used in this paper are helpful for overcoming difficulties arising from the nonlinearity and coupling and lead to a related theoretical analysis for nonlinear FI schemes. [Copyright &y& Elsevier]

An automated general purpose method is introduced for computing a rigorous estimate of a bounded region in ℝ n whose points satisfy a given property. The method is based on calculations conducted in interval arithmetic and the constructed approximation is built of rectangular boxes of variable sizes. An efficient strategy is proposed, which makes use of parallel computations on multiple machines and refines the estimate gradually. It is proved that under certain assumptions the result of computations converges to the exact result as the precision of calculations increases. The time complexity of the algorithm is analyzed, and the effectiveness of this approach is illustrated by constructing a lower bound on the set of parameters for which an overcompensatory nonlinear Leslie population model exhibits more than one attractor, which is of interest from the biological point of view. This paper is accompanied by efficient and flexible software written in C++ whose source code is freely available at . [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space. The analytical solution and approximate solution are represented in terms of series. For any initial function , we prove , , . Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective. [Copyright &y& Elsevier]

Abstract: In the present paper, we propose a hierarchical identification method (SSHI) for solving Lyapunov matrix equations, which is based on the symmetry and skew-symmetry splitting of the coefficient matrix. We prove that the iterative algorithm consistently converges to the true solution for any initial values with some conditions, and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factors appropriately. Furthermore, we show that the method adopted can be easily extended to study iterative solutions of other matrix equations, such as Sylvester matrix equations. Finally, we test the algorithms and show their effectiveness using numerical examples. [Copyright &y& Elsevier]

Abstract: A matrix is said to be a symmetric orthogonal matrix if . A matrix is said to be generalized centro-symmetric (generalized central anti-symmetric) with respect to , if (). The generalized centro-symmetric matrices have wide applications in information theory, linear estimate theory and numerical analysis. In this paper, we propose a new iterative algorithm to compute a generalized centro-symmetric solution of the linear matrix equations . We show, when the matrix equations are consistent over generalized centro-symmetric matrix , for any initial generalized centro-symmetric matrix , the sequence generated by the introduced algorithm converges to a generalized centro-symmetric solution of matrix equations . The least Frobenius norm generalized centro-symmetric solution can be derived when a special initial generalized centro-symmetric matrix is chosen. Furthermore, the optimal approximation generalized centro-symmetric solution to a given generalized centro-symmetric matrix can be derived. Several numerical examples are given to show the efficiency of the presented method. [Copyright &y& Elsevier]

In this paper, we study the equivalence characterizations of several modified fixed-point equations to variational inequalities (VI). Based on these equations, we give some applications in constructing iterative methods for the solution of the VI. Especially, we show global convergence, the sublinear convergence, and the finite termination of a new iterative algorithm under certain conditions. [Copyright &y& Elsevier]