浮点乘法器中IEEE舍入的实现

描述了浮点乘法器中舍入的基本方法,介绍了一种实现舍入的系统的设计方法和硬件模型,并对它进行了分析,在这种系统设计方法的基础上,提出了一种直接预测和选择的舍入方案。     

浮点乘法器中的舍入方法研究

文章针对浮点乘法器中的尾数舍入方法进行了研究,提出了一种基于预测和选择的快速舍入方法。相对于传统的舍入方法,这种方法通过预测和选择来实现快速舍入,舍入过程相对简单,减小了实现时的硬件开销和关键路径延时,明显地提高了浮点乘法器的性能,并且精度越高,性能提高的空间越大。     

Optimal discrete sizing of truss structures subject to buckling constraints

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with conservative regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.     

A Newton method for solving continuous multiple material minimum compliance problems

This paper presents an implementation of an active-set line-search Newton method intended for solving large-scale instances of a class of multiple material minimum compliance problems. The problem is modeled with a convex objective function and linear constraints. At each iteration of the Newton method, one or two linear saddle point systems are solved. These systems involve the Hessian of the objective function, which is both expensive to compute and completely dense. Therefore, the linear algebra is arranged such that the Hessian is not explicitly formed. The main concern is to solve a sequence of closely related problems appearing as the continuous relaxations in a nonlinear branch and bound framework for solving discrete minimum compliance problems. A test-set consisting of eight discrete instances originating from the design of laminated composite structures is presented. Computational experiments with a branch and bound method indicate that the proposed Newton method can, on most instances in the test-set, take advantage of the available starting point information in an enumeration tree and resolve the relaxations after branching with few additional function evaluations. Discrete feasible designs are obtained by a rounding heuristic. Designs with provably good objective functions are presented.     

A fast algorithm for local feature selection in data classification

Typical feature selection methods select a global feature subset that is applied over all regions of the sample space. In localized feature selection (LFS), each region of the sample space is associated with its own optimized feature subset. This allows the feature subset to adapt to local variations in the sample space. Feature subsets are selected such that within a localized region, within‐class distances are minimized and between‐class distances are maximized. LFS outperforms global feature selection methods. LFS is solved using a randomized rounding approach when weights of regions are fixed. Randomized rounding is a too time‐consuming algorithm. In this paper, we show that LFS has a closed‐form solution when weights of regions are fixed. Using this closed‐form solution can decrease the runtime of solving LFS substantially. Experimental results on real datasets confirm that the classification error rate of our proposed method and the randomized rounding‐based method are the same; the runtime of our proposed method is much better than that of the randomized rounding‐based method; and the classification error rate of our proposed method and the randomized rounding‐based method outperforms the state‐of‐the‐art feature selection methods.     

Shortest Path Geometric Rounding

Exact implementations of algorithms of computational geometry are subject to exponential growth in running time and space. In particular, coordinate bit-complexity can grow exponentially when algorithms are cascaded : the output of one algorithm becomes the input to the next. Cascading is a significant problem in practice. We propose a geometric rounding technique: shortest path rounding . Shortest path rounding trades accuracy for space and time and eliminates the exponential cost introduced by cascading. It can be applied to all algorithms which operate on planar polygonal regions, for example, set operations, transformations, convex hull, triangulation, and Minkowski sum. Unlike other geometric rounding techniques, shortest path rounding can round vertices to arbitrary lattices, even in polar coordinates, as long as the rounding cells are connected. (Other rounding techniques can only round to the integer grid.) On the integer grid, shortest path rounding introduces less combinatorial change and geometric error than the other rounding methods. Three algorithms are given for shortest path rounding, one of which we have used in industrial application software since 1992. In combination with recent advances in exact floating point evaluation of numerical primitives, shortest path geometric rounding yields a practical solution to numerical issues in computational geometry. Geometric algorithms can be implemented exactly on floating point input coordinates; the exact output coordinates can be rounded to accurate floating point approximations; and the cost of each arithmetic operation is only a little more than if it were implemented as a single hardware floating point operation. Received February 7, 1997; revised September 9, 1998.     

On the validity of using small positive lower bounds on design variables in discrete topology optimization

It is proved that an optimal {ε, 1} ⁿ solution to a “ε-perturbed” discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to {0, 1} ⁿ , to the corresponding “unperturbed” discrete problem, provided that the constraints in the perturbed problem are carefully defined and ε > 0 is sufficiently small.     

Improved form of the conjugate gradient method

The conjugate gradient method, which is used for solving systems of linear algebraic equations, is studied. A notation for the method has been found, which proved to be the simplest and the most resistant to rounding errors. A criterion is constructed for the end of iterations based on the prevalence of rounding errors. Numerical calculations are made illustrating the specifics of the method convergence for well- and ill-posed problems. The generalization of this form is written for problems with preconditioning.     

Anisotropic Filtering of Non-Linear Surface Features

A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non‐linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well‐known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non‐linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.     

Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

求解整数非线性规划结合正交杂交的离散PSO 算法

针对整数非线性规划问题,提出一种结合正交杂交的离散粒子群优化(PSO)算法.首先采用舍入取整方法,为了减少舍入误差,对PSO中的每个粒子到目前为止的最好位置进行随机修正,将基于正交实验设计的正交杂交算子引入离散PSO算法,以增强搜索性能;然后对PSO算法中的惯性权重和收缩因子采用动态调整策略,以提高算法的搜索效率;最后对一些不同维数的整数非线性规划问题进行数值仿真实验,实验结果表明了所提出算法的有效性.     

Implementation of digital controllers

The variance of error at the output of a digital control system due to input data quantization and product rounding in a digital controller is derived. Two forms of controller implementations are considered. Then an expression for the word length that yields a specified variance of error is determined. Scaling is then discussed and an example consisting of a discrete integral plus proportional controller is presented.     

Recursive central rounding for mixed integer programs

We introduce a new rounding heuristic for mixed integer programs. Starting from a fractional solution, the new approach is based on recursively fixing a subset of the discrete variables while using the analytic center to re-center the remaining ones. The proposed rounding approach can be used independently or integrated with other heuristics. We demonstrate both setups by first using the proposed approach to round the optimal solution of the linear programming relaxation. We then integrate the proposed rounding heuristic with the feasibility pump by replacing the original simple rounding function of the feasibility pump. We conduct computational testing on mixed integer problems from MIPLIB and CORAL and on mixed integer quadratic problems from MIQPLIB. The proposed algorithm is computationally efficient and provides good quality feasible solutions.     

Reconstruction of 2D polygonal curves and 3D triangular surfaces via clustering of Delaunay circles/spheres

A simple and efficient method is presented in this paper to reliably reconstruct 2D polygonal curves and 3D triangular surfaces from discrete points based on the respective clustering of Delaunay circles and spheres. A Delaunay circle is the circumcircle of a Delaunay triangle in the 2D space, and a Delaunay sphere is the circumsphere of a Delaunay tetrahedron in the 3D space. The basic concept of the presented method is that all the incident Delaunay circles/spheres of a point are supposed to be clustered into two groups along the original curve/surface with satisfactory point density. The required point density is considered equivalent to that of meeting the well-documented r-sampling condition. With the clustering of Delaunay circles/spheres at each point, an initial partial mesh can be generated. An extrapolation heuristic is then applied to reconstructing the remainder mesh, often around sharp corners. This leads to the unique benefit of the presented method that point density around sharp corners does not have to be infinite. Implementation results have shown that the presented method can correctly reconstruct 2D curves and 3D surfaces for known point cloud data sets employed in the literature.     

Efficient computation of high-order Meixner moments for large-size signals and images analysis

In this paper, we present an in-depth study on the computational aspects of high-order discrete orthogonal Meixner polynomials (MPs) and Meixner moments (MMs). This study highlights two major problems related to the computation of MPs. The first problem is the overflow and the underflow of MPs values (“Nan” and “infinity”). To overcome this problem, we propose two new recursive Algorithms for MPs computation with respect to the polynomial order n and with respect to the variable x. These Algorithms are independent of all functions that are the origin the numerical overflow and underflow problem. The second problem is the propagation of rounding errors that lead to the loss of the orthogonality property of high-order MPs. To fix this problem, we implement MPs based on the following orthogonalization methods: modified Gram-Schmidt process (MGS), Householder method, and Givens rotation method. The proposed Algorithms for the stable computation of MPs are efficiently applied for the reconstruction and localization of the region of interest (ROI) of large-sized 1D signals and 2D/3D images. We also propose a new fast method for the reconstruction of large-size 1D signal. This method involves the conversion of 1D signal into 2D matrix, then the reconstruction is performed in the 2D domain, and a 2D to 1D conversion is performed to recover the reconstructed 1D signal. The results of the performed simulations and comparisons clearly justify the efficiency of the proposed Algorithms for the stable analysis of large-size signals and 2D/3D images.

     

Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition

This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented.     

基于近似模型的多层模糊CMAC自适应非线性控制

针对非线性离散时间系统的控制问题,提出了一种基于近似模型的多层模糊CMAC 自适应控制方法.采用多层模糊CMAC对非线性函数进行逼近,并提出了一种新的神经网络学 习算法来保证权值的有界性.由于无需满足PE条件,所以文中提出的方法对于离散时间系统 的神经网络控制问题具有实际价值.     

Calibration of an smt robot assembly cell

A new calibration method for an assembly robot cell is described. The proposed method is a combination of a model-free, numerical, relative robot calibration procedure and a procedure for the robot periphery calibration. Two important simplifications based on the study of an assembly process are introduced into the calibration strategy. A robot is calibrated in a task (Cartesian) space. The robot workspace and the number of calibrated degrees of freedom (dof) in the task space are reduced in accordance with the difficulty measure of the task. An automatic measurement system for measuring the relative robot accuracy was developed. An original principle of transforming the robot endpoint approach distance into the one-dimensional position displacement error is introduced. The accuracy errors of each particular calibrated dof in the task space is measured separately. The error tables are used in a direct robot calibration procedure that is based on the linear interpolation of the discrete position-error functions. An iterative inverse calibration algorithm used in a particular robot cell is described. An efficient sensor-based system for an additional simultaneous robot periphery calibration is presented. The implementation of the proposed calibration methodology in the pick-and-place robot cell for Surface Mount Technology (SMT) is presented. © 1994 John Wiley & Sons, Inc.     

基于离散傅里叶不变特征的人脸识别

给出了一种基于离散傅里叶不变特征的人脸识别方法。从连续傅里叶变换出发,讨论连续傅里叶变换情况下的傅里叶变换性质,给出离散傅里叶变换情况下的傅里叶变换性质。依据离散傅里叶变换性质,推导出离散傅里叶变换的不变特征,并将其用于人脸图像识别。人脸识别结果表明方法具有很好的识别能力。     

A computing capability test for a switched system control design using the Haris-Rogers method

The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these systems.Many solutions have been proposed,most of which are based on finding the existence of a common Lyapunov function(CLF) or a multiple Lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been presented.This method is seen to be less computationally taxing compared to methods based on solving LMIs.To substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test case.From the obtained solutions,the validity of the controllers and the corresponding CLF was verified.It was found that all tested solvers were able to correctly solve the LIs.The issue of rounding-off error in numerical computation based software is discussed in detail.The test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal precision.The use of different external solvers led to the same conclusion in terms of the stability of switched systems.As a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested.