一类矩阵方根的直接表达式

本文对特征值在复平面上任意一边界线过原点的半平面上的矩阵,给出级数形式的方根公式,这种公式用矩阵本身直接表达其方根。作为特例,我们得到了正定矩阵的正定 p 次方根的直接求法。     

Recursive estimation and forecasting of non-stationary time series

The paper presents a unified, fully recursive approach to the modelling and forecasting of non-stationary time-series. The basic time-series model, which is based on the well-known ‘component’ or ‘structuraL’ form, is formulated in state-space terms. A novel spectral decomposition procedure, based on the exploitation of recursive smoothing algorithms, is then utilized to simplify the procedures of model identification and estimation. Finally, the fully recursive formulation allows for conventional or self-adaptive implementation of state-space forecasting and seasonal adjustment. Although the paper is restricted to the consideration of univariate time series, the basic approach can be extended to handle explanatory variables or full multivariable (vector) series.     

纱条不匀时序模型的建立

采用Pandit Wu方法对并条纱条进行建模分析 ,提高了建模过程的程序化水平 ,可迅速建立在线预测模型。研究认为 ,并条纱条可以用AR(n)模型及ARMA(m ,n)模型进行预测控制 ,且模型的阶次一般为 2～ 5。     

3-距离空间中一类压缩映象序列的公共不动点定理

引入3－距离空间的概念，给出3－距离空间中一类压缩映象序列的公共不动点定理。     

等速输送运动纱线的横向振动分析

本文讨论在非齐次边界条件下由端点运动激励的纱线强迫振动问题。首先讨论了相应的齐次方程的特征值问题,给出了两端无横动时等速移动(即等速输送运动)纱线的各阶固有频率与复振型函数。然后,利用傅立叶级数理论寻求非齐次边界条件下的齐次方程的解,从而求出了等速输送纱线在卷绕端运动激励下的稳态响应的精确解。     

动态数据系统(DDS)建模方法的改进

本文概述了原DDS建模方法的缺点,叙述了改进的途径,推导了改进的算法,给出了改进部分的详细框图。首先用长自回归拟合数据直到残差为白噪声,如AR模型阶不高,则认定为AR模型。否则,利用数据和残差,线性估计ARMA模型参数。增阶和降阶时,Yule—Wolker方程系数阵和模型参数都可递推求得。初估ARMA模型后,用非线性最小二乘法来优化参数。通过二个实例计算表明,经改进的方法可以节省66％的机时,效果是明显的。     

关于二元傅立叶级数的收敛性

本文选取一组求和因子ρα、β，得到一个新的二元傅立叶级数的部分和算子Ｓｎｍ（ｆ；ｘ，ｙ），使它的范数等于Ｏ（１）。     

基于双向差分的船舶横摇时间序列的预报

根据船舶在随机海浪作用下的运动特性,基于双向差分算法建立模型,并运用于船舶横摇运动时间序列的预报,取得较好的效果.该模型也可用于纵摇、艏摇的时间序列的预报.     

Estimation procedures for structural time series models

A univariate structural time series model based on the traditional decomposition into trend, seasonal and irregular components is defined. A number of methods of computing maximum likelihood estimators are then considered. These include direct maximization of various time domain likelihood function. The asymptotic properties of the estimators are given and a comparison between the various methods in terms of computational efficiency and accuracy is made. The methods are then extended to models with explanatory variables.