Mehar’s methods for fuzzy assignment problems with restrictions

In this paper, limitations of existing methods [5, 11] for solving fuzzy assignment problems (FAPs) are pointed out. In order to overcome the limitations of existing methods, two new methods named Mehar’s methods are proposed. To show the advantages of Mehar’s methods over existing methods, some FAPs are solved. The Mehar’s methods can solve the problems solved by existing methods as well as those which cannot be solved by existing methods.     

几类改进的新的两步六阶Chebyshev-Halley方法

利用权函数法,给出非线性方程求根的Chebyshev-Halley方法的几类改进方法,证明方法六阶收敛到单根.Chebyshev-Halley方法的效率指数为1.442,改进后的两步方法的效率指数为1.565.最后给出数值试验,且与牛顿法,Chebyshev-Halley 方法及其它已知的方程求根方法做了比较.结果表明方法具有一定的优越性.     

Applications of doubly companion matrices

Doubly companion matrices are used as a tool to analyze the ESIRK and DESIRE methods, and the general linear methods satisfying the IRKS property. These methods can be considered as extensions of the DIRK and SIRK Runge–Kutta methods, and were introduced to overcome some of the undesirable properties of these methods. A connection between the ESIRK and DESIRE methods, and IRKS methods is also established. Several low order methods are given.     

Waveform Relaxation Methods for Lie-Group Equations

In this paper, we derive and analyse waveform relaxation (WR) methods for solving differential equations evolving on a Lie-group. We present both continuous-time and discrete-time WR methods and study their convergence properties. In the discrete-time case, the novel methods are constructed by combining WR methods with Runge-Kutta-Munthe-Kaas (RK-MK) methods. The obtained methods have both advantages of WR methods and RK-MK methods, which simplify the computation by decoupling strategy and preserve the numerical solution of Lie-group equations on a manifold. Three numerical experiments are given to illustrate the feasibility of the new WR methods.     

Interior-point methods for linear programming: a review

The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with infeasible interior methods and homogeneous self-dual methods for linear programming. Also discussed are some theoretical issues in interior-point methods like dependence of complexity bounds on some non-traditional measures different from the input length L of the problem. Finally, the paper concludes with remarks on the comparison of interior-point methods with the simplex method based on their performance on NITLIB suite, a standard collection of test problems.     

On interval predictor-corrector methods

One can approximate numerically the solution of the initial value problem using single or multistep methods. Linear multistep methods are used very often, especially combinations of explicit and implicit methods. In floating-point arithmetic from an explicit method (a predictor), we can get the first approximation to the solution obtained from an implicit method (a corrector). We can do the same with interval multistep methods. Realizing such interval methods in floating-point interval arithmetic, we compute solutions in the form of intervals which contain all possible errors. In this paper, we propose interval predictor-corrector methods based on conventional Adams-Bashforth-Moulton and Nyström-Milne-Simpson methods. In numerical examples, these methods are compared with interval methods of Runge-Kutta type and methods based on high-order Taylor series. It appears that the presented methods yield comparable approximations to the solutions.     

Preservation of equilibria for symplectic methods applied to Hamiltonian systems

In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In par- ticular, three classes of symplectic methods are considered： symplectic Runge-Kutta （SRK） methods, symplectic partitioned Runge-Kutta （SPRK） methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points uncondi- tionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.     

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.     

The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides

In this paper, we introduce two new methods for solving large sparse nonsymmetric linear systems with several right-hand sides. These methods are the global Hessenberg and global CMRH methods. Using the global Hessenberg process, these methods are less expensive than the global FOM and global GMRES methods [9]. Theoretical results about the new methods are given, and experimental results that show good performances of these new methods are presented.     

QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

1. IntroductionInvestigating whether a numerical method inherits some dynamical properties possessed bythe differential equation systems being integrated is an important field of numerical analysisand has received much attention in recent years See the review articlesof Sanz-Serna[9] and Section 11.16 of Hairer et. al.[2] for more detail concerning the symplectic methods. Most of the work on canonical iotegrators has dealt with one-step formulaesuch as Runge-Kutta methods and Runge'methods …     

New Multivalue Methods for Differential Algebraic Equations

Multivalue methods are slightly different from the general linear methods John Butcher proposed over 30 years ago. Multivalue methods capable of solving differential algebraic equations have not been developed. In this paper, we have constructed three new multivalue methods for solving DAEs of index 1, 2 or 3, which include multistep methods and multistage methods as special cases. The concept of stiff accuracy will be introduced and convergence results will be given based on the stage order of the methods. These new methods have the diagonal implicit property and thus are cheap to implement and will have order 2 or more for both the differential and algebraic components. We have implemented these methods with fixed step size and they are shown to be very successful on a variety of problems. Some numerical experiments with these methods are presented.     

Local error estimation for multistep collocation methods

Multistep collocation methods for initial value problems in ordinary differential equations are known to be a subclass of multistep Runge-Kutta methods and a generalisation of the well-known class of one-step collocation methods as well as of the one-leg methods of Dahlquist. In this paper we derive an error estimation method of embedded type for multistep collocation methods based on perturbed multistep collocation methods. This parallels and generalizes the results for one-step collocation methods by Nørsett and Wanner. Simple numerical experiments show that this error estimator agrees well with a theoretical error estimate which is a generalisation of an error estimate first derived by Dahlquist for one-leg methods.     

变分不等式的几类求解方法

本文转为系统地分析和概述了变分不等式问题中几类占有重要地位的求解方法,包括方法产生的背景,主要结果及应用等,这几类算法分别为连续算法,（拟）牛顿型算法,一般迭代模型,投影算法,投影收缩算法等。     

Computation of Carlson's Multiple Hypergeometric Function R for Bayesian Applications

Abstract

Carlson's multiple hypergeometric functions arise in Bayesian inference, including methods for multinomial data with missing category distinctions and for local smoothing of histograms. To use these methods one needs to calculate Carlson functions and their ratios. We discuss properties of the functions and explore computational methods for them, including closed form methods, expansion methods, Laplace approximations, and Monte Carlo methods. Examples are given to illustrate and compare methods.     

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 second-order periodic initial-value problems. In comparison with some methods in [1-4,6], the advantage of these methods has a higher accuracy and minimal phase-lag. 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]. second order periodic initial-value problems, phase-lag, local truncation error     

Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems

To the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.     

Convergence results for general linear methods on singular perturbation problems

Many numerical methods used to solve Ordinary Differential Equations, or Differential Algebraic Equations can be written as general linear methods. The B-convergence results for general linear methods are for algebraically stable methods, and therefore useless for nearly A-stable methods. The purpose of this paper is to show convergence for singular perturbation problems for the class of general linear methods without assuming A-stability.     

互补问题算法的新进展

互补问题是一类重要的优化问题，在最近３０多年的时间里，人们为求解它而提出了许多算法，该文主要介绍１９９０－１９９７年之间出现的某些新算法，它们大致可归类为：（１）光滑方程法；（２）非光滑方程法；（３）可微无约束优化法；（４）ＧＬＰ投影法；（５）内点法；（６）磨光与非内点连续法，文中对每类算法及相应的收敛性结果做了描述与评论，并列出有关文献。     

Direct prediction methods in Hilbert space with applications to control problems

In this paper, the convergence of variable-metric methods without line searches (direct prediction methods) applied to quadratic functionals on a Hilbert space is established. The methods are then applied to certain control problems with both free endpoints and fixed endpoints. Computational results are reported and compared with earlier results. The methods discussed here are found to compare favorably with earlier methods involving line searches and with other direct prediction quasi-Newton methods.     

Expanding stability regions of explicit advective-diffusive finite difference methods by Jacobi preconditioning

Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions that are placed on stable time-step intervals. Stability bounds for explicit time differencing methods on advective–diffusive problems are generally determined by the diffusive part of the problem. These bounds are very small and implicit methods are used instead. The linear systems arising from these implicit methods are generally solved by iterative methods. In this article we develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods. A Jacobi preconditioned time differencing method is defined and analyzed for both diffusion and advection–diffusion equations. Several computational examples of both linear and nonlinear advective-diffusive problems are solved to demonstrate the accuracy and improved stability limits. © 1995 John Wiley & Sons, Inc.