LOCAL ERROR ESTIMATES FOR METHODS OF CHARACTERISTICS INCORPORATING STREAMLINE DIFFUSION

Allen and Liu (1995) introduced a new method for a time-dependent convection dominated diffusion problem, which combines the modified method of characteristics and method of streamline diffusion. But they ignored the fact that the accuracy of time discretization decays at half an order when the characteristic line goes out of the domain. In present paper, the author shows that, as a remedy, a simple lumped scheme yields a full accuracy approximation. Forthermore, some local error bounds independent of the small viscosity axe derived for this scheme outside the boundary layers.

AModified Search and Rescue Optimization Based Node Localization Technique inWSN

Wireless sensor network(WSN)is an emerging technology which find useful in several application areas such as healthcare,environmentalmonitoring,border surveillance,etc.Several issues that exist in the designing of WSN are node localization,coverage,energy efficiency,security,and so on.In spite of the issues,node localization is considered an important issue,which intends to calculate the coordinate points of unknown nodes with the assistance of anchors.The efficiency of the WSN can be considerably influenced by the node localization accuracy.Therefore,this paper presents a modified search and rescue optimization based node localization technique(MSRONLT)forWSN.The major aim of theMSRO-NLT technique is to determine the positioning of the unknown nodes in theWSN.Since the traditional search and rescue optimization(SRO)algorithm suffers from the local optima problemwith an increase in number of iterations,MSRO algorithm is developed by the incorporation of chaotic maps to improvise the diversity of the technique.The application of the concept of chaotic map to the characteristics of the traditional SRO algorithm helps to achieve better exploration ability of the MSRO algorithm.In order to validate the effective node localization performance of the MSRO-NLT algorithm,a set of simulations were performed to highlight the supremacy of the presented model.A detailed comparative results analysis showcased the betterment of the MSRO-NLT technique over the other compared methods in terms of different measures.

SEMIPARAMETRIC REGRESSION MODELS WITH LOCALLY GENERALIZED GAUSSIAN ERROR'S STRUCTURE

This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Engineering and applied mathematics disciplines that involve differential equations in general,and initial value problems in particular,include classical mechanics,thermodynamics,electromagnetism,and the general theory of relativity.A reliable,stable,efficient,and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential equations.In this study,the tangent slope is assumed to be the contra-harmonic mean,in which the arithmetic mean is used as a correction instead of Euler’s method to improve the efficiency of the improved Euler’s technique for solving ordinary differential equations with initial conditions.The stability,consistency,and efficiency of the system were evaluated,and the conclusions were supported by the presentation of numerical test applications in engineering.According to the stability analysis,the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value problems.To validate the rate convergence of the numerical technique,a few initial value problems of both scalar and vector valued types were examined.The proposed method,modified Euler explicit method,and other methods known in the literature have all been used to calculate the absolute maximum error,absolute error at the last grid point of the integration interval under consideration,and computational time in seconds to test the performance.The Lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed method.The method is determined to be more reliable than the commonly existing methods with the same order of convergence,as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed,Mat Lab-R2011b has been used.

A joint optimization algorithm for focused energy delivery in precision electronic warfare

Focused energy delivery(FED) is a technique that can precisely bring energy to the specific region,which arouses wide attention in precision electronic warfare(PREW).This paper first proposes a joint optimization model with respect to the locations of the array and the transmitted signals to improve the performance of FED.As the problem is nonconvex and NP-hard,particle swarm optimization(PSO) is adopted to solve the locations of the array,while designing the transmitted signals under a feasible array is considered as a unimodular quadratic program(UQP) subproblem to calculate the fitness criterion of PSO.In the PSO-UQP framework established,two methods are presented for the UQP subproblem,which are more efficient and more accurate respectively than previous works.Furthermore,a threshold value is set in the framework to determine which method to adopt to take full advantages of the methods above.Meanwhile,we obtain the maximum localization error that FED can tolerate,which is significant for implementing FED in practice.Simulation results are provided to demonstrate the effectiveness of the joint optimization algorithm,and the correctness of the maximum localization error derived.

A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

THE HIGH ACCURACY EXPLICIT DIFFERENCE SCHEME FOR SOLVING PARABOLIC EQUATIONS 3-DIMENSION

In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.

Optimized Deep Learning Model for Fire Semantic Segmentation

Recent convolutional neural networks(CNNs)based deep learning has significantly promoted fire detection.Existing fire detection methods can efficiently recognize and locate the fire.However,the accurate flame boundary and shape information is hard to obtain by them,which makes it difficult to conduct automated fire region analysis,prediction,and early warning.To this end,we propose a fire semantic segmentation method based on Global Position Guidance(GPG)and Multi-path explicit Edge information Interaction(MEI).Specifically,to solve the problem of local segmentation errors in low-level feature space,a top-down global position guidance module is used to restrain the offset of low-level features.Besides,an MEI module is proposed to explicitly extract and utilize the edge information to refine the coarse fire segmentation results.We compare the proposed method with existing advanced semantic segmentation and salient object detection methods.Experimental results demonstrate that the proposed method achieves 94.1%,93.6%,94.6%,95.3%,and 95.9%Intersection over Union(IoU)on five test sets respectively which outperforms the suboptimal method by a large margin.In addition,in terms of accuracy,our approach also achieves the best score.

A MULTIPLE INTELLIGENT AGENT SYSTEM FOR CREDIT RISK PREDICTION VIA AN OPTIMIZATION OF LOCALIZED GENERALIZATION ERROR WITH DIVERSITY

Company bankruptcies cost billions of dollars in losses to banks each year. Thus credit risk prediction is a critical part of a bank＇s loan approval decision process. Traditional financial models for credit risk prediction are no longer adequate for describing today＇s complex relationship between the financial health and potential bankruptcy of a company. In this work, a multiple classifier system （embedded in a multiple intelligent agent system） is proposed to predict the financial health of a company. In our model, each individual agent （classifier） makes a prediction on the likelihood of credit risk based on only partial information of the company. Each of the agents is an expert, but has limited knowledge （represented by features） about the company. The decisions of all agents are combined together to form a final credit risk prediction. Experiments show that our model out-performs other existing methods using the benchmarking Compustat American Corporations dataset.

OPTIMAL INTERIOR AND LOCAL ERROR ESTIMATES OF A RECOVERED GRADIENT OF LINEAR ELEMENTS ON NONUNIFORM TRIANGULATIONS

We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.

EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y"=f(x,y)

A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and efficient than some methods proposed in [1-3,10].

TWO-STEP SCHEME FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations(BSDEs).A necessary and sufficient condition is given to judge the L 2-stability of our numerical schemes.This stochastic linear two-step method possesses a family of 3-order convergence schemes in the sense of strong stability.The coefficients in the numerical methods are inferred based on the constraints of strong stability and n-order accuracy(n∈N^(+)).Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.

Shamanskii-Like Levenberg-Marquardt Method with a New Line Search for Systems of Nonlinear Equations

To save the calculations of Jacobian,a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fa.Its convergence properties have been proved by using a trust region technique under the local error bound condition.However,the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction.For this purpose,the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence.Under the same condition as trust region case,the convergence rate also has been shown to be m+1 by using this line search technique.Numerical experiments show the new algorithm can save much running time for the large scale problems,so it is efficient and promising.

Numerical Integration Over Implicitly Defined Domains with Topological Guarantee

Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions.In this paper,we use interval arithmetic to identify the boundary of the integration domain exactly,thus getting the correct topology of the domain.Furthermore,a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost.Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.

Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method.Part II:Higher-Order Schemes

Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this paper.The Cartesian cut-stencil FD method,which employs 1-D quadratic transformation functions to map a non-uniform(uncut or cut)physical stencil to a uniform computational stencil,can be combined with compact HO Pad´e-Hermitian formulations to produce HO cut-stencil schemes.The modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO formulations.The effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are discussed.The numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.

HIGH-ACCURACY EXPLICIT TWO-STEP METHODS WITH MINIMAL PHASE-LAG FOR y″=f(t,y)

In this paper, two families of high accuracy explicit two-step methods with minimal phase-lag are developed for the numerical integration of special secondorder periodic initial-value problems. In comparison with some methods in [1, 4,6], the advantage of these methods has a higher accuracy and minimal phaselag. The methods proposed in this paper can be considered as a generalization of some methods in [1,3,4]. Numerical examples indicate that these new methods are generally more accurate than the methods used in [3,6].

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.