基于最小二乘法的曲线拟合及其简化算法

文章简述了最小二乘法曲线拟合的原理,给出了正规方程组的公式推导过程.针对最小二乘法曲线拟合中系数求解的运算量过大问题,以及自变量为自然数序列的情况,通过推导多项式拟合的计算公式得出了一种简化算法,并结合单片机这种运算能力比较小的应用场合,给出了可以减少计算步骤的简化计算公式,根据简化后的计算公式可以快速计算出所需要的系数.最后以一组实验数据进行了实际计算的例证,该简化算法计算过程简单,计算结果精确,可以广泛应用于控制器的数据采集与处理系统中.     

Fitting computers into design

Computer Aided Design is only one part of the design process and in order to achieve satisfactory utilisation of computers it is necessary to identify their appropriate role in design. This paper presents the way in which CAD fits into Engineering Design, as outlined to students, and a selection of typical exercises and projects undertaken in this context.     

基于最小拟合误差平方和准则的空间聚类

在一些回归分析问题中，数据来自于空间对象的非空间属性．许多问题中不用考虑空间属性，而直接分析非空间属性．如果在整个问题空间中，对象空间差异较大，需要将空间对象划分为若干子空间，子空间对应的局域回归模型，可以减小空间差异性的影响．针对子空间连通性约束情况下空间对象的局域回归分析问题，提出基于最小拟合误差平方和准则的空间划分方法，从一个空间的初始划分开始，按照拟合误差平方和下降的原则调整子空间边界，获得新的空间划分和对应的回归模型，不断迭代直到准则函数收敛．     

基于小波分析的最小二乘拟合及应用

直线是图像分析过程中非常重要的描述符号。在工业控制中,图像处理通常采用最小二乘法对直线进行拟合,但在对估计精度要求较高时,传统最小二乘法往往不能满足要求。将离散小波变换和传统最小二乘法相结合,建立了一种基于小波预处理的最小二乘估计的新方法,获得了比传统最小二乘法效果更好的估计结果。试验证明了该方法的有效性和高精度性。     

基于JavaScript技术在最小二乘法拟合上的实现

本文提出了一种基于JavaScript脚本语言实现最小二乘法拟合的方式,通过转置矩阵、逆矩阵等相关矩阵运算,得到结果向量,即可求出需要的系数常量。实验采用自由落体原理公式进行数据拟合,最后得到的g值精确度达到小数点后15位,符合预期目标。这种在客户端浏览器实现最小二乘法拟合的方式使考研人员摆脱了安装专门软件的繁琐,使实现矩阵运算、最小二乘法拟合变得简单。     

Rail Detection Based on LSD and the Least Square Curve Fitting

It is necessary to rely on the rail gauge to determine whether the object beside the track will affect train operation safety or not. A convenient and fast method based on line segment detector (LSD) and the least square curve fitting to identify the rail in the image is proposed in this paper. The image in front of the train can be obtained through the camera on-board. After preprocessing, it will be divided equally along the longitudinal axis. Utilizing the characteristics of the LSD algorithm, the edges are approximated into multiple line segments. After screening the terminals of the line segments, it can generate the mathematical model of the rail in the image based on the least square. Experiments show that the algorithm in this paper can fit the rail curve accurately and has good applicability and robustness.

     

基于最小二乘曲线拟合的信号调理电路误差补偿方法

在自动测试系统中,常常需要信号调理模块对输出或者输入信号进行调理,而由于信号调理电路的非线性及零漂常常会大大影响系统精度,对信号调理部分的误差进行分析并进行软件补偿是很有必要的;提出了一种基于最小二乘曲线拟合方法的信号调理电路误差补偿方法,应用该方法可以得到信号调理电路的误差曲线,进行补偿后可以大大降低信号调理电路的误差,提高系统精度。     

基于乘积型最小二乘法的传感器特性拟合

本文提出一种基于乘积型最小二乘法的传感器特性拟合方法 ,模型参数反映传感器非线性特性和漂移特性。这种方法具有计算量小 ,适于便携式仪表的软件补偿 ,应用实践表明 :这种方法是切实可行的。     

一种基于最小二乘估计的玻壳曲面拟合方法

位移传感器测量已经成为一种重要的测量手段。为估计一种基于线性可变差动传感器(LVDT)玻壳测试系统的质量,用最小二乘法对测试曲面进行球面拟合,得到相对应的玻壳曲面。利用该曲面计算曲率半径,检验各位移传感器(LVDT)安装是否准确,从而测试生产的玻壳是否合格,并利用坐标值即可对系统进行系统误差的校正。由于最小二乘法可削弱误差较大的点的影响,根据其特点建立数学模型进行拟合,其结果对6寸玻壳的生产加工环节具有更直接的指导意义。     

最小二乘法直线拟合数据处理的VB程序设计

利用Visual Basic语言实现对数据的最小二乘法处理,使数据处理非常方便且可靠性高,避免了大量的计算过程,保证数据处理的质量和效果.     

最小二乘法直线拟合数据处理的VB程序设计

利用Visual Basic语言实现对数据的最小二乘法处理,使数据处理非常方便且可靠性高,避免了大量的计算过程,保证数据处理的质量和效果.     

最小二乘拟合与形态学膨胀的图像数率可分级编码算法

本文提出一种基于最小二乘的线性拟合和形态学膨胀操作的小波域图像数率可分级编码算法,该算法利用图像小波变换子带中的零树结构系数间的对应关系,利用最小二乘线性拟合方法通过对父亲系数和间接后代系数的线性拟合确定直接后代的重要系数。同时通过对重要系数进行数学形态学的膨胀操作,形成重要系数的聚簇,从而降低重要系数位置的同步信息。来提高图像的编码效率。实验结果表明,在低码率下,解码后的图像较EZW和MRWD具有更好的峰值信噪比。     

相图与相关热力学性质的综合分析方法

本文发展了一种将相图和其它相关的热力学性质放在一起关联的综合方法并实现了计算机程序化。该方法基于广义最小二乘原理,可以同时考虑多种不同来源、不同性质的原始数据,于同一拟合过程中得到所有的未知参数。结果,能够更加充分合理地利用原始数据,提取更多的信息,并且保证拟合结果在体系内彼此相容。对于线性拟合,文中给出一种由焓项、熵项和其他项三个加权部分构成的通用拟合关系式,以用于常见各类热力学性质和相平衡数据的变换。文中还给出回归Marquart二步参数优化法的结构框图和若干应用实例。     

Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms

In this paper we deal with two geometric problems arising from heterogeneous parallel computing: how to partition the unit square into p rectangles of given area s ₁ , s ₂ , . . . ,s _p (such that Σ _i=1 ^p s _i = 1 ), so as to minimize either (i) the sum of the p perimeters of the rectangles or (ii) the largest perimeter of the p rectangles? For both problems, we prove NP-completeness and we introduce a 7/4 -approximation algorithm for (i) and a $(2/\sqrt{3})$ -approximation algorithm for (ii).     

Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms

   Abstract. In this paper we deal with two geometric problems arising from heterogeneous parallel computing: how to partition the unit square into p rectangles of given area s ₁ , s ₂ , . . . ,s _p (such that Σ _i=1 ^p s _i = 1 ), so as to minimize either (i) the sum of the p perimeters of the rectangles or (ii) the largest perimeter of the p rectangles? For both problems, we prove NP-completeness and we introduce a 7/4 -approximation algorithm for (i) and a

Holes in joins

A join of two relations in real databases is usually much smaller than their Cartesian product. This means that most of the combinations of tuples in the crossproduct of the respective relations do not appear together in the join result. We characterize these combinations as ranges of attributes that do not appear together. We sketch an algorithm for finding such combinations and present experimental results from real data sets. We then explore two potential applications of this knowledge in query processing. In the first application, we model empty joins as materialized views, we show how they can be used for query optimization. In the second application, we propose a strategy that uses information about empty joins for an improved join selectivity estimation.     

正交几何椭圆拟合与代数拟合及椭圆定义的迭代拟合的比较分析

通过把正交几何椭圆拟合与代数拟合和椭圆定义的迭代拟合进行比较分析,考虑到原有拟合存在的缺陷,充分应用正交的概念及最小二乘法(LS)原理和方法的优点,对椭圆进行正交的几何拟合。实验表明,正交几何拟合很好地弥补了其它拟合方法的缺陷,取得良好的效果。     

Fitting superellipses

In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. This paper describes and tests several fitting techniques which provide different trade-offs between efficiency and accuracy. In addition, we describe various alternative error of fit measures that can be applied by most superellipse fitting methods     

The Square

Geometer Rachel Fletcher explores the ratio associated with the regular quadrilateral figure known as the square, looking at the square’s inherent symbolism and the four-ness of the cross and the tetractys, as she constructs ad quadratum and other geometric techniques.