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This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance. [ABSTRACT FROM AUTHOR]

Highlights • A new variational model for image retinex is proposed. • The existence of minimizer for the variational model is proved. • An efficient algorithm is derived to solve the model by adding auxiliary variables. • The convergence of the numerical algorithm is proved under some assumptions. • The proposed method can be extended to other regularization and fidelity terms. Abstract In this paper, we propose a detail preserving variational model for Retinex to simultaneously estimate the illumination and the reflectance from an observed image. Most previous models use the log-transform as pretreatment which results in loss of details in reflectance. From this observation, a detail preserving variational method is proposed for better decomposition. Different from the log-transform based models, the proposed model performs the decomposition directly in the image domain. Mathematically, we prove the existence of a solution for the proposed model. Numerically, we derive an efficient iterative algorithm by utilizing alternating direction method of multipliers (ADMM) method. Experimental results demonstrate the effectiveness of the proposed method. Compared with other closely related Retinex methods, the proposed method achieves competitive results on both subjective and objective assessments. [ABSTRACT FROM AUTHOR]

Abstract: In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor–corrector Euler–Maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path. This paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions. A natural analogue of the -stability criterion is studied. Numerical examples are given to illustrate the computational efficiency of the new predictor–corrector Euler–Maruyama approximation. [Copyright &y& Elsevier]

In this paper, we investigate a discretized version of an elliptic optimal control problem which is presented by Stadler (2009). An alternating direction method is proposed to solve this problem and demonstrated as globally convergent. This class of methods is attractive due to its simplicity and thus is adequate for solving large-scale problems. The preliminary numerical results present the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze the Levenberg–Marquardt method for solving system of absolute value equations A x − | x | = b , where A ∈ R n × n , b ∈ R n and x ∈ R n are unknown. We present different line search methods to convey the main idea and the significant modifications. We discuss the convergence of the proposed method. We consider numerical examples to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction. [ABSTRACT FROM AUTHOR]

In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical solution of a nonstandard Sturm-Liouville boundary value problem on the half line where the coefficients of the differential terms depend on the unknown function by means of a scalar integral operator. By using a finite difference discretization, a truncated quadrature rule and an iterative procedure, we construct a numerical method, whose convergence is proved. The order of convergence and the truncation at infinity are also discussed. Finally, some numerical tests are given to show the performance of the method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical approximation of elliptic interface problems via isoparametric finite element methods. First, a convergence analysis is carried which asserts that optimal rates of convergence are recovered in both the energy and the L 2 –norms. Subsequently, the efficiency of isoparametric finite elements for the problem at hand is also assessed via numerical experiments. Results both with smooth and piecewise regular interfaces are presented and discussed. The numerical predictions corroborate the theoretical results and they also indicate that second-order convergence is achieved in the L ∞ -norm. Comparisons between isoparametric finite elements, Lagrangian finite elements and the Immersed Interface Method are also performed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a-priori error estimates for problems involving curved interfaces and solved with the linear or quadratic extended finite-element method (X-FEM), with particular emphasis on the influence of the geometry representation and the quadrature. We focus on strong discontinuity problems, which covers the case of holes in a material or cracks not subjected to contact as the main applications. The well-known approximation of the curved geometry based on the interpolated level-set function and straight linear or curved quadratic subcells is used, whose accuracy is quantified by means of an appropriate error measure. A priori error estimates are then derived, which depend upon the interpolation order of the displacement, and foremost upon the above error measure and the quadrature scheme in the subcells. The theoretical predictions are successfully compared with numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: The numerical method proposed in this paper is an improvement of the ADI method by Li and Mayo (1994). The proposed method is unconditionally stable for both two and three-dimensional heat conduction interface problems, while Li’s ADI method is only stable for two-dimensional problems. The method is a modification of a Locally One-Dimensional (LOD) difference scheme, with correction term added to the right-hand side of the standard LOD difference scheme at irregular points. The correction term is determined so that the local truncation error is of order at irregular points. Then the method is two-order convergent in both time and space directions. Numerical examples show good agreement with exact solutions and confirm the order of convergence and stability. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical method for solving a class of fractional variational problems (FVPs) with multiple dependent variables, multi order fractional derivatives and a group of boundary conditions. The fractional derivative in the problem is in the Caputo sense. In the presented method, the given optimization problem reduces to a system of algebraic equations using polynomial basis functions. An approximate solution for the FVP is achieved by solving the system. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [Copyright &y& Elsevier]

Abstract: The discrete mollification method is a convolution-based filtering procedure suitable for the regularization of ill-posed problems. Combined with explicit space-marching finite difference schemes, it provides stability and convergence for a variety of coefficient identification problems in linear parabolic equations. In this paper, we extend such a technique to identify some nonlinear diffusion coefficients depending on an unknown space dependent function in one dimensional parabolic models. For the coefficient recovery process, we present detailed error estimates and to illustrate the performance of the algorithms, several numerical examples are included. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of Center Based Genetic Algorithm (CBGA) is proposed to overcome the premature convergence and to solve the stiffness equivalence problem. With the information of population center, central chaotic mutation and space shrinking strategy are designed to guide the evolutionary searching process. Meanwhile, the rank value based roulette selection and a new Cauchy preferential crossover operator are collaboratively used with the mutation operators in the CBGA. To avoid the loss of the best solution, the elitist strategy is employed as well. In addition, local search is embedded in the CBGA after the main evolutionary search process to enhance the exploitation ability by further improving the elite solution. Numerical simulation and comparison based on a set of benchmark functions show that, the proposed CBGA is superior to the hybrid genetic algorithm from the literature in terms of searching efficiency, solution quality, robustness and success ratio. Finally, CBGA is applied to successfully solve the stiffness equivalence problem of the small-aspect-ratio aircraft wing to tapered beam. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Numerical examples involving smooth and singular data are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an interval version of the generalized accelerated overrelaxation methods, which we refer to as IGAOR, for solving the linear complementarity problems, LCP (M, q), and develop a class of multisplitting IGAOR methods which can be easily implemented in parallel. In addition, in regards to the H-matrix with positive diagonal elements, we prove the convergence of these algorithms and illustrate their efficiency through our numerical results. [Copyright &y& Elsevier]

Abstract: An improved version of rectangular method (IRM) is introduced in this paper to numerically solve the stochastic Volterra equation (SVE). We focus on studying the order of error between the numerical and exact solutions, which is improved to . Furthermore, an explicit form of the IRM scheme is introduced and its convergence is established. A numerical example has also been presented to show the feasibility of the methods. [ABSTRACT FROM AUTHOR]

Abstract: The coupling of cell-centered finite volume method with primal discontinuous Galerkin method is introduced in this paper for elliptic problems. Convergence of the method with respect to the mesh size is proved. Numerical examples confirm the theoretical rates of convergence. Advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new nonmonotone trust-region method of conic model for solving unconstrained optimization problems. Both the local and global convergence properties are analyzed under reasonable assumptions. Numerical experiments are conducted to compare this method with some existed ones which indicate that the new method is efficient. [Copyright &y& Elsevier]

Abstract: In this paper, based on a simple model of the trust region subproblem, we propose a new self-adaptive trust region method with a line search technique for solving unconstrained optimization problems. By use of the simple subproblem model, the new method needs less memory capacitance and computational complexity. And the trust region radius is adjusted with a new self-adaptive adjustment strategy which makes full use of the information at the current point. When the trial step results in an increase in the objective function, the method does not resolve the subproblem, but it performs a line search technique from the failed point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective and attractive for large-scale optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, a new trust region algorithm is proposed for solving unconstrained optimization problems. This method can be regarded as a combination of trust region technique, fixed step-length and ODE-based methods. A feature of this proposed method is that at each iteration, only a system of linear equations is solved to obtain a trial step. Another is that when a trial step is not accepted, the method generates an iterative point whose step-length is defined by a formula. Under some standard assumptions, it is proven that the algorithm is globally convergent and locally superlinear convergent. Preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: This paper proves the convergence of some generalized Schwarz algorithms for solvingthe obstacle problems with a T-monotone operator. Numerical results show that the generalized Schwarz algorithms converge faster than the classical Schwarz algorithms. [Copyright &y& Elsevier]