On Chebychev Acceleration Procedures for Alternating Direction Iterative Methods

The solution of large sparse systems of linear equations arising,for example, from the numerical solution of elliptic partialdifferential equations is considered, with reference to theacceleration technique commonly known as Chebychev acceleration.In particular its application to alternating direction iterative(A.D.I.) methods is compared with the more standard techniquessuch as successive overrelaxation. It is conjectured that inmost circumstances a suitable A.D.I. strategy is that of applyingChebychev semiiteration to an A.D.I. process with a single A.D.I.parameter. It is shown that under general conditions this procedure maysometimes produce faster convergence than the usual multiparameterA.D.I. procedure.     

Optimum Extrapolated Alternating Direction Implicit Schemes in the Presence of Singular Matrices

This paper shows how Extrapolated Alternating Direction Implicit(E.A.D.I.) methods can be used for the numerical solution ofLaplace's equation under Neumann boundary conditions. E.A.D.I.methods are applied with the Douglas set of parameters and optimumE.A.D.I. schemes are given.     

Alternating Direction Methods for a System of Parabolic Equations in Two Space Dimensions with a Mixed Derivative

An alternating direction (A.D.I.) method, which requires thesolution of two block tridiagonal sets of equations at eachtime step, is suggested for solving a system of parabolic equationswith variable coefficients in two space dimensions with a mixedderivative. The method is shown to be unconditionally stablefor two semi-infinite ranges of an auxiliary parameter subjectto restrictions on the coefficient matrices. Other existingfinite difference schemes are mentioned and numerical resultsare presented.     

The numerical solution of a model problem biharmonic equation by using Extrapolated Alternating Direction Implicit methods

The numerical solution of the 2-dimensional biharmonic equation over the unit square by using Extrapolated Alternating Direction Implicit (E.A.D.I.) methods is studied. To approximate the biharmonic equation both a 13-point and a 25-point difference replacements are considered. In each case E.A.D.I. schemes are used together with the acceleration parameter fixed during the iterations or varying according to the Douglas set of parameters. Finally optimum E.A.D.I. schemes are given for every value of the numberN of mesh subdivisions in each co-ordinate direction.     

Numerical Solution of the Robin Problem by Extrapolated A. D. I. Methods

In this paper the Robin problem for elliptic equations is consideredand its numerical integration by several variants of the Extrapolatedform of the Alternating Direction Implicit (E.A.D.I.) methodsis discussed. A comparison among the E.A.D.I. variants includedhere as well as those studied in an earlier paper is carriedout.     

Improved extrapolated alternating direction implicit schemes for the numerical solution of three-dimensional elliptic problems

This paper shows how a further improvement on the convergence rates of Extrapolated Alternating Direction Implicit (E.A.D.I.) Schemes for the numerical solution of the Poisson equation over the unit cube can be achieved. Several E.A.D.I. methods are examined, optimum parameters are found in each case and a comparison of the various methods is made. Two worked characteristic numerical examples prove the validity of the theory developed.Mr. Krimnianiotis' part of the work was sponsored by the National Foundation of Research under contract No 276/77.     

Bianchi surfaces in R3 and deformation of hyperelliptic curves

New solutions of the problem of describing hyperbolic surfaces of specified negative Gaussian curvature are obtained. The answer is given in terms of 9 functions.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 78–88, September, 1992.The first author (D. A. K.) wishes to express his appreciation to A. I. Bobenko for useful discussion.     

High Accuracy A.D.I. Methods for Hyperbolic Equations with Variable Coefficients

High accuracy alternating direction implicit (A.D.I.) methodsare derived for solving the wave equation with variable coefficientsin one, two, and three space dimensions. Splittings are discussedand numerical results presented.     

High accuracy A.D.I. methods for fourth order parabolic equations with variable coefficients

High accuracy alternating direction implicit (A.D.I.) methods are derived for solving fourth order parabolic equations with variable coefficients in one, two, and three space dimensions. Splittings are discussed and numerical results are presented.     

High accuracy A.D.I. methods for parabolic equations with variable coefficients

Summary High accuracy alternating direction implicit (A.D.I.) methods are derived for solving the heat conduction equation with variable coefficients in two and three space dimensions. These methods are shown to be unconditionally stable.     

Lessons for O.R. from A.I.: A Scheduling Case Study

This paper compares operational research (O.R.) with the currently fashionable topic of artificial intelligence (A.I.) at a detailed level. A.I. concepts, techniques and history are summarized, and O.R. and A.I. approaches compared. A case study-the development of a potential aid to scheduling repair jobs on RAF squadrons—is described. The paper shows where A.I. concepts and techniques were used in the prototype program, known as the Fault Identification & Expediting Repair (FIXER) system. Finally, some lessons for O.R. are drawn.     

The Application of the Automatic Interaction Detector (A.I.D.) Programme and Multiple Regression Techniques to the Assessment of Store Performance and Site Selection

The paper begins with an examination of the gravity model approach to site selection and concludes that there are certain practical limitations which make it unsuitable for predicting the distribution of consumers' expenditure amongst individual outlets.It then describes how a combination of the Automatic Interaction Detector (A.I.D.) and multiple regression techniques can be used to provide criteria for judging the performance of a chain of retail outlets and assessing the potential of new sites. A feature of the approach is the measurement of approximately fifty factors which may influence turnover and the inclusion of attitudinal data, derived from a sample survey of shoppers, quantifying factors such as the appearance and image of a store. The method has been successfully applied to supermarkets, durable goods outlets, off-licences, chemists, building societies and car washes.     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析

研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计.     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

Finite elements for transonic potential flows

A finite element method is used for the computation of entropy solutions to the transonic full potential equation. Physically correct solutions with sharp and correctly placed shocks were obtained. (AMS (MOS) 1980 Mathematics subject classifications: 65N30, 76N15, 35M05, 76H05, 49D10, 35A40, 35L67.)     

A Linear Programming Model for an Integrated Crop and Intensive Beef Production Enterprise

In an integrated crop and intensive beef production enterprise, some of the feedstuffs used for cattle feeding are grown by the enterprise. In evaluating the performance of operations of this type, the interactions between the crop and beef production parts of the enterprise must be taken into account. A linear programming (L.P.) model of this type of enterprise is developed, with the coefficients of the animal feeding activities being derived from a dynamic programming (D.P.) model. This D.P. model is used to determine the least-cost method of feeding animals to produce a specified liveweight gain using rations formulated by L.P. from a given set of feedstuffs. This approach allows the interactions between crop and livestock production to be taken into account without the need to make assumptions about the source of feedstuffs or the rate of liveweight gain.     

Periodic unfolding and homogenizationÉclatement périodique et homogénéisation

A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures). To cite this article: D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104.     

The brightness of the zenith sky during twilight

A visual photometer is described for measuring the brightness of the zenith sky during twilight. The results of measurements made with it at Bombay on a large number of clear moonless evenings during the period December 1937 to March 1938 are discussed. A red filter RG₁ (Schott and Gen.) and a green filter VG₁ (Schott and Gen.) were used. With the latter, it was possible to continue observations even when twilight conditions had completely ceased. The variations in brightness agree with a relation proposed by Link, namely,dI/I=β sin θ sec² θdθ, where I is the brightness of the zenith sky, θ the angular depression of the sun below the horizon and β a constant. If the brightness is due only to primary scattering from the atmosphere illuminated by sunlight, it is possible to connect β with the temperature of the atmospheric layer responsible for the scattering. The difficulty however is to ascertain to what extent secondary scattering is important.     

Environmental Impact Assessment and Decision Analysis

A brief introduction to environmental impact assessment (E.I.A.) is given. An E.I.A. requires, as a final stage, the aggregation of diverse and highly subjective impacts, though in practice this is often done implicitly. Explicit aggregation techniques have their origins in cost-benefit analysis or decision analysis, and the appropriateness of these two techniques for applications in E.I.A.s is considered.An illustration of decision analysis is given in which multi-attribute value analysis is used to assist in the siting of new mines. The method can be presented as a development of the simple visual sieving technique, and by employing colour graphics facilities and microcomputers, a portable, flexible and powerful decision aid emerges: but powerful tools require careful handling.