关键词： Forecasting   Geological Phenomena   Geology   Models, Theoretical   Water Movements   Water Movements   Water Supply   Water Supply  

摘要： Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

关键词： variety of Lie algebras   covariant   invariant   deformation   degeneration  

摘要： We give an algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras from the representation theoretic viewpoint. For this purpose, we give the GL(V)-irreducible decomposition of the polynomial ring of the space V-2* circle times V (V = C-4) up to degree 3, and show that intrinsic concepts defined by the vanishing of these covariants are sufficient to distinguish the isomorphism classes. As an application, we describe the variety of 4-dimensional Lie algebras and their degenerations in a comparatively simple form, by introducing a new family of normal forms of 4-dimensional Lie algebras that are just fitted for these purposes. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： “万物皆数”   “万物皆算法”   科学数学化   数理自然观   数理科学观  

摘要： 文章以科学数学化为线索 ,阐述了科学数学化的思想根源、发展历程和各阶段的特点 。

关键词： 模糊神经网络   快速参数学习算法   T-S模糊推理系统   多层前向神经网络   改进RLS算法  

摘要： 提出了一种新的模糊神经网络的快速参数学习算法 ,采用一些特殊的处理 ,可以用递推最小二乘法 (RLS)来调整所有的参数 .以前的学习算法在调整模糊隶属度函数的中心和宽度的时候 ,用的是梯度下降法 ,具有容易陷入局部最小值点、收敛速度慢等缺点 ,而本算法则可以克服这些缺点 ,最后通过仿真验证了算法的有效性 .

关键词： 数学选择题   高考题   估算法  

摘要： 高考数学选择题,题目多,分值高.对其中的一些计算型题目,如果循规蹈矩、按步就班地演算——小题大作,势必费时费力,影响整套试卷的完成.如果针对题目的特点,施行合乎情理的“估算”,则可快速获解.本文结合近几年高考数学选择题,谈谈“估算法”的应用技巧. 一、选择特值、特例、特殊位置估算 1.选取特值估算 例1(2000年春季高考题)函数y=1/(2+sinx+cosx)的最大值是( ).

关键词： ASYMPTOTIC expansions   RICCATI equation  

摘要： In this paper we study a continuous-time multiparameter algebraic Riccati equation (MARE) with an indefinite sign quadratic term. The existence of a unique and bounded solution of the MARE is newly established. We show that the Kleinman algorithm can be used to solve the sign indefinite MARE. The proof of the convergence and the existence of the unique solution of the Kleinman algorithm is done by using the Newton-Kantorovich theorem. Furthermore, we present new algorithms for solving the generalized multiparameter algebraic Lyapunov equation (GMALE) by means of the fixed-point algorithm. (C) 2002 Elsevier Science (USA).

关键词： 小学数学   教学设计   “加、减法的一些简便算法”  

关键词： Kleinman algorithm   singular perturbed systems   Newton-Kantorovich theorem   generalized algebraic Lyapunov equation  

摘要： In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be indefinite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton-Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method to solve the generalized algebraic Lyapunov equation (GALE) appearing in the Kleinman algorithm is given. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： ALGORITHMS   CYLINDRIC algebras  

摘要： We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions (cad). Such adjacencies constitute a basis for determining all other cell adjacencies. Our new algorithms are local, being applicable to a specified 0D cell and the 1D cells described by specified polynomials. Particularly efficient algorithms are given for the 0D cells in spaces of dimensions two, three and four. Then an algorithm is given for a space of arbitrary dimension. This algorithm may on occasion report failure, but it can then be repeated with a modified isolating interval and a likelihood of success. (C) 2002 Elsevier Science Ltd.

关键词： risk management   algorithm architectures   combinatorics  

摘要： Increased information intensity is greatly expanding the importance of model-based decision-making in a variety of areas. This paper reviews applications that involve large-scale combinatorics, data uncertainty, and game theoretic considerations and describes three related algorithm architectures that address these features. In particular, highly customized mathematical programming architectures are discussed for time-based problems involving significant combinatorial character. These architectures are then embedded into a simulation-based optimization (SIMOPT) architecture to address both combinatorial character and significant data uncertainty. Multiple SIMOPT objects are combined using a coordinating architecture to address game theoretic issues. A key focus of the paper is a discussion of the algorithm engineering principles necessary to mitigate the NP-complete nature of practical problems. The life cycle issues of algorithm delivery, control, support, and extensibility are important to sustained use of advanced decision-making technology. An inductive development methodology provides a means for developing sophisticated algorithms that become increasingly powerful as they are subjected to new constraint combinations. Implicit generation of formulations is crucial to routine large-scale use of mathematical programming based architectures. (C) 2002 Elsevier Science Ltd. All rights reserved.