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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]

Abstract In this paper, a preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problems associated with an M -matrix is proposed. The convergence analysis of the presented method is given. In particular, we provide a comparison theorem between preconditioned two-step modulus-based Gauss–Seidel (PTMGS) iteration method and two-step modulus-based Gauss–Seidel (TMGS) iteration method, which shows that PTMGS method improves the convergence rate of original TMGS method for linear complementarity problem. Numerical tested examples are used to illustrate the theoretical analysis. [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]

This paper is concerned with strong convergence of a tamed theta scheme for neutral stochastic differential delay equations with one-sided Lipschitz drift. Strong convergence rate is revealed under a global one-sided Lipschitz condition, while for a local one-sided Lipschitz condition, the tamed theta scheme is modified to ensure the well-posedness of implicit numerical schemes, then we show the convergence of the numerical solutions. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified Newton–Traub composition with increasing order of convergence for solving systems of nonlinear equations. The idea is based on the recent development by Sharma et al. (2015). Analysis of convergence shows that the presented method has sixth order of convergence. Computational efficiency of the new method is considered and compared with some well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed method. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. The basins of attraction of existing methods and the presented method are given to demonstrate their performance. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze a unified model of two-step iterative method for solving a system of nonlinear equations. We prove that the unified model achieves fourth order convergence. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods. From the comparison with some known methods it is observed that the present methods are of practical utility. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partitioned PSB method for solving partially separable unconstrained optimization problems. By using a projection technique, we construct a sufficient descent direction. Under appropriate conditions, we show that the partitioned PSB method with projected direction is globally and superlinearly convergent for uniformly convex problems. In particular, the unit step length is accepted after finitely many iterations. Finally, some numerical results are presented, which show that the partitioned PSB method is effective and competitive. [ABSTRACT FROM AUTHOR]

The neutron transport equation in the integral form is of difficult solution and therefore, schemes for obtaining an equivalent differential formulation are used. In this paper is used the discrete ordinates method (S N method) in order to obtain the equivalent differential formulation. Inspired in the GLS method (Galerkin least square method) a variant of the GLS (Brooks and Hughes, 1982; Ern and Guermond, 2004; Johnson, 1990) method denoted GpLS (Galerkin partial least-square) is proposed for solving this equivalent differential formulation. The convergence rates as well as the robustness of GLS method are preserved by the GpLS method that possesses computational lower cost. Simulations comparing the convergence rates of GpLS method with other methods are presented, confirming the best performance of GpLS method. The numerical experiments were made using fixed source in multiplying medium, with the objective to test the robustness of GpLS method. All the numerical experiments presented confirm the good properties of approximation of GpLS method. [ABSTRACT FROM AUTHOR]

In order to solve large sparse saddle point problems (SPP) quickly and efficiently, Wang and Zhang recently studied the preconditioned accelerated Hermitian and skew-Hermitian splitting (PAHSS) methods. Through accelerating the PAHSS iteration algorithms by using parameterized Uzawa (PU) method, a preconditioned AHSS-PU alternating splitting iterative method (PAHSS-PU method) for solving saddle point problems is proposed in this paper. The convergence results of this new method are given under some suitable conditions. Moreover, we can obtain that if the parameters are suitable selected, then the PAHSS-PU algorithm will outperform the PAHSS algorithm and some Uzawa-type methods in the same precision condition. Numerical experiments are presented to illustrate the theoretical results and examine the numerical effectiveness of the PAHSS-PU method. [ABSTRACT FROM AUTHOR]

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]

This paper proposes a predictor–corrector primal–dual modified log-barrier interior–exterior point method with global convergence and cubic fitting strategies for solving the Reactive Optimal Power Flow (ROPF) problem. The interior–exterior approach is a variant of the primal–dual nonlinear rescaling method, recently proposed. The application of the global convergence strategy produces only descent directions, even if the optimization problem is non-linear and non-convex. The application of a cubic fitting strategy for modified log-barrier functions preserve the continuity and also the first and second-order derivatives of the logarithm near the boundary of the feasible set. Some updating rules for the Lagrange multiplier estimates are theoretically and numerically evaluated. Numerical tests and comparisons with classical interior point methods, involving the electrical systems of 3, 9, IEEE-14, IEEE-30, IEEE-57, IEEE-118, IEEE-162 and IEEE-300 buses, are performed, which demonstrate the robustness and efficiency of the method. [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 definition of weighted statistical convergence was first introduced by Karakaya & Chishti (2009) and later on Mursaleen et al. (2012) modified the definition of this concept. Using the modified definition, Edely et al. (2013) had researched further in approximation theory for periodic functions and Belen & Mohiuddine (2013) had further extended to the new-definition of weighted λ -statistical convergence. But some problems are still there, so the definition of weighted λ -statistical convergence is needed to modify. In this paper, we will introduce some new constraints which will make the definition of weighted λ -statistical convergence is more useful by using the definition of αβ -statistical convergence. Using it and independently, some newly developed concepts of the convergence of a sequence of random variables in probability, namely, weighted modulus αβ -statistical convergence of order γ , weighted modulus αβ -strong Cesáro convergence of order γ , weighted modulus S α β -convergence of order γ , and weighted modulus N α β -convergence of order γ , have been introduced and their basic interrelations also have been investigated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective. [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]