借助Matlab遗传算法反演火山区压力源参数

首先分析了Mogi模型的经典最小二乘反演由于出现矩阵奇异或接近奇异而发散的局限性,决定采用具有全局高效搜索性和优化计算时不需要求导的遗传算法来反演火山区压力源参数。反演程序调用Matlab7.0 Release14工具箱中的选择、交叉和变异等相关程序。最后应用该程序和长白山天池火山区水准和GPS观测资料联合反演火山区压力源参数,经过比较遗传算法和阻尼最小二乘方法的反演结果,可看出2种方法结果近似,可见此方法方便快捷地实现了目标函数的最小化。     

LabVIEW在曲线拟合中的应用研究

介绍了LabVIEW中用于曲线拟合的子模块，对各子模块的曲线拟合理论作了介绍，重点介绍了非线性Lev-Mar拟合理论，并以例子辅助说明．     

最小二乘法在石油闪点检测中的应用

以铂电阻分度函数为基础，利用最小二乘法算法，给出了拟合多项式，很好地解决了石油闪点检测系统中铂电阻不平衡电桥法测温方案中的非线性误差，其方便性和实用性已在应用中得到验证。     

Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

用“多化一”最小二乘法建立吸附动力学方程

用若干个一元最小二乘法，建立多元经验公式；以吸附动力学方程为例，取得了预期的结果。     

选择最小方差阈值的判别式方法

本文阐述了选择最小方差阈值的各次累积矩判别式方法,证明了零次矩判别式最小方差阈值选择法在理论上可使统计累积矩的次数降到最低,在实用上可进一步减少运算量。     

偏最小二乘紫外分光光度法同时测定萘，1－甲基萘和蒽

用偏最小二乘法（ＰＬＳ）进行校正和预测，不经分离同时测定了混合体系中的萘，１－甲基萘和蒽。萘，１－甲基萘和蒽的浓度分别在０～２８ｍｇ／Ｌ，０～４０ｍｇ／Ｌ和０～４０ｍｇ／Ｌ的浓度范围服从比耳定律。对合成样品中这三种组分进行分析，结果令人满意。     

最小二乘解存在的充分必要条件

本文提出了当观测值的权矩阵为正定或半正定的前提下，其最小二乘解存在的充分必要条件为并以间接平差为例验证了该结论的正确性。     

On some significance tests in cluster analysis

We investigate the properties of several significance tests for distinguishing between the hypothesisH of a homogeneous population and an alternativeA involving clustering or heterogeneity, with emphasis on the case of multidimensional observationsx ₁, ...,x _n ^p . Four types of test statistics are considered: the (s-th) largest gap between observations, their mean distance (or similarity), the minimum within-cluster sum of squares resulting from a k-means algorithm, and the resulting maximum F statistic. The asymptotic distributions underH are given forn and the asymptotic power of the tests is derived for neighboring alternatives.     

多维位置数据最优融合方法

本文给出了一种多传感器多维位置数据融合的方法。这种方法基于多维位置数据的鲁棒估计和最小方差结合法。每个传感器用鲁棒估计得到自身数据的位置估计和方差估计,把这些估计融合为一个最优估计,即传感器系统的估计。