Solving SDGE Models: A New Algorithm for the Sylvester Equation

This paper presents a new numerical algorithm for solving the Sylvester equation involved in higher-order perturbation methods developed for solving stochastic dynamic general equilibrium models. The new algorithm surpasses other methods used so far (including the very popular doubling algorithm) in terms of computational time, memory consumption, and numerical stability.     

Solving Rational-Expectations Models through the Anderson-Moore Algorithm: An Introduction to the Matlab Implementation

The Anderson-Moore algorithm provides a well-established solution method for systems of linear rational expectations equations. The purpose of this paper is to support a wider use of the algorithm by describing two sets of Matlab routines that allow its practical implementation. The emphasis is on the structures that should be modified to tailor the programs to one’s needs. I present the application of the algorithm for the solution of a version of [Coenen, G. and V. Wieland, ECB Working Paper, No. 30 (2000)]’s macroeconometric model of the Euro area.JEL Classification: C88; E17; C63     

Solving Infinite Horizon Growth Models with an Environmental Sector

This paper concerns computational models in environmental economics andpolicy, particularly so-called integrated assessment models. For themost part, such models are simply extensions of standard neoclassicalgrowth models, extended by including the environment and pollutiongeneration. We review the structure of integrated assessment models,distinguishing between finite horizon and infinite horizon models, bothdeterministic and stochastic. We present a new solution algorithm forinfinite horizon integrated assessment models, relying on a neural netapproximation of the value function within an iterative version of theBellman equation.     

Solving Dynamic Economic Models with Nonconvexities Due to Fixed Costs

An algorithm is developed for solving nonlinear dynamic models in which one of the control variables is discrete. This structure is particularly relevant to economic models with fixed costs. The methodology is a generalization of discrete state space Euler equation methods for solving dynamic models.     

Quadrature-Based Methods for Solving Heterogeneous Agent Models with Discontinuous Distributions

The paper develops a method for solving heterogeneous agent models in which the distribution of characteristics across agents is a state variable and the distribution can be discontinuous at points that vary endogenously. The method extends the approach of [Tauchen, George and Robert Hussey, Econometrica 59, 1991, 371–396] for solving nonlinear rational expectations models using a discrete-state Markov chain approximation to a continuous Markov process. The paper presents an example application of a general equilibrium labor search model with persistence in the idiosyncratic productivity of heterogeneous firms.JEL classification: C63, C68, J64     

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.     

可重构的光总线并行计算模型及其算法

介绍几种典型可重构光总线并行计算模型及其高效的基本操作与并行算法,使人们更加了解光总线并行计算模型及优越性,为今后进一步研究光总线模型及其并行算法奠定基础。     

求最小期望权值强循环规划解

现实世界中,动作的执行通常都要耗费一定的代价,且由于外界环境的干扰,动作执行后的结果具有不确定性.针对这一问题,对不确定状态转移系统的动作赋予权值,使用概率分布表示状态转换的随机性,提出了强循环规划解的期望权值,并且设计了求最小期望权值强循环规划解的方法.该方法的主要思想是使用深度优先搜索求出规划问题的所有强循环规划解,再将强循环规划解分别转换成以状态到目标状态的期望权值为变元的线性方程组,最后使用高斯消元法解方程组,从而找出最小期望权值强循环规划解.     

Computer-based techniques for solving problems of applied and computational mathematics with given quality characteristics

The paper is concerned with computer-based techniques for the choice and development of computational resources and their efficient use to find an approximate solution with a given accuracy in a limited processor time. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 33–41, September–October 2006.     

The Complexity of Learning According to Two Models of a Drifting Environment

We show that a bound on the rate of drift of the distribution generating the examples is sufficient for agnostic learning to relative accuracy , where c > 0 is a constant; this matches a known necessary condition to within a constant factor. We establish a sufficient condition for the realizable case, also matching a known necessary condition to within a constant factor. We provide a relatively simple proof of a bound of + on the sample complexity of agnostic learning in a fixed environment.     

Learning Occupancy Grid Maps with Forward Sensor Models

This article describes a new algorithm for acquiring occupancy grid maps with mobile robots. Existing occupancy grid mapping algorithms decompose the high-dimensional mapping problem into a collection of one-dimensional problems, where the occupancy of each grid cell is estimated independently. This induces conflicts that may lead to inconsistent maps, even for noise-free sensors. This article shows how to solve the mapping problem in the original, high-dimensional space, thereby maintaining all dependencies between neighboring cells. As a result, maps generated by our approach are often more accurate than those generated using traditional techniques. Our approach relies on a statistical formulation of the mapping problem using forward models. It employs the expectation maximization algorithm for searching maps that maximize the likelihood of the sensor measurements.     

基于混合粒子群算法的高维优化问题求解

为解决高维复杂函数的优化问题，克服标准粒子群算法早熟收敛、局部搜索能力弱等缺点，在标准粒子群优化算法中融合了遗传算法的设计思想，提出了一种新颖的混合粒子群算法。高维函数个别维上的差解导致算法最终无法找到全局最优解，而通常的优化算法很难寻找到每一维上的最佳值。受遗传算法思想的启发，在粒子的进化过程中，通过对最优粒子的每一维进行评价，找到导致最终解质量差的维度，对其维上的数据进行变异，进而有针对性地改进，寻找到每一维上的最佳位置。对典型高维复杂函数的仿真表明：算法在求解质量和求解速度两方面都得到了好的结果。     

可变数据重用因子仿射投影算法

从修改传统仿射投影算法（Affine Projection Algorithm,APA）的约束条件出发,推导出了一种新的可变数据重用因子仿射投影算法。该算法解决了传统APA算法收敛速度与稳态失调和计量复杂度之间的矛盾,实现了在初始阶段数据重用因子大,收敛后数据重用因子小的目标。仿真结果表明该算法最终达到了高数据重用因子APA的收敛速度和NLMS算法的计算量和稳态失调。     

Data‐driven high‐order terminal iterative learning control with a faster convergence speed

In this paper, a novel high‐order optimal terminal iterative learning control (high‐order OTILC) is proposed via a data‐driven approach for nonlinear discrete‐time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high‐order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high‐order OTILC to outperform the low‐order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is data‐driven in which no explicit models are used except for the input and output data. The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed‐batch fermentater demonstrate the effectiveness of the proposed high‐order OTILC design.     

Parallel Strategies for Solving SURE Models with Variance Inequalities and Positivity of Correlations Constraints

The problem of computing estimates of parameters in SURE models withvariance inequalities and positivity of correlations constraintsis considered. Efficient algorithms that exploit the blockbi-diagonal structure of the data matrix are presented. Thecomputational complexity of the main matrix factorizations isanalyzed. A compact method to solve the model with proper subsetregressors is proposed.     

On the Solution of Boundary Value Problems by Using Fast Generalized Approximate Inverse Banded Matrix Techniques

A class of finite difference schemes in conjunction with approximate inverse banded matrix techniques based on the concept of LU-type factorization procedures is introduced for computing fast explicit approximate inverses. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of banded linear systems. A theorem on the rate of convergence and estimates of the computational complexity required to reduce the L-norm of the error is presented. Applications of the method on linear and non-linear systems are discussed and numerical results are given.     

Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Photosimulation: Interreflection with Arbitrary Reflectance Models and Illumination

Methods for realistic image synthesis are described. Exact mathematical establishment of reflectance models is presented, together with the development of feasible reflectance models meeting the energy balance. A new bidirectional reflectance type, separable reflectance, is introduced. Necessary and sufficient conditions for the iterative solution of the linear equation system of interreflection are presented. Lastly, a new method of inserting numerically defined objects into real optical surroundings is described.     

含多状态时滞的连续时间迭代学习控制系统稳定性分析

探讨了含多状态时滞连续时间迭代学习控制系统的稳定性分析问题, 尤其是当系统参数带有多面体不确定性时的鲁棒稳定性分析问题. 通过引入一个扩展算子, 利用迭代学习控制中的二维分析方法给出了时滞系统整个学习动态过程的连续离散Roesser系统描述. 基于所得的Roesser系统, 首先利用二维系统理论给出了保证迭代学习控制系统渐近稳定的充要条件, 然后结合鲁棒H∞控制理论提出了以线性矩阵不等式形式描述的充分条件来保证迭代学习控制系统的单调收敛性. 结果表明, 通过求解线性矩阵不等式确定的学习增益可以使控制输入误差随着迭代次数的增加单调收敛于零. 仿真结果表明, 通过增加满足一组线性矩阵不等式条件的P型学习增益能够使得一个鲁棒渐近稳定的迭代学习控制方案变为鲁棒单调收敛的, 同时还可以大大提高收敛速率.