Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

终身寿险纯保费的精算方法

以终身寿险为例,运用概率论和数理统计方法对几种不同情况下趸交、年交和月交纯保费的精算方法进行详细剖析,并给出相应的计算公式。     

酚醛树脂泡沫材料的填充改性及其性能研究

用氢氧化铝粉末对泡沫酚醛树脂材料进行填充改性,并对其主要性能进行研究．结果表明,填充改性能提高酚醛泡沫材料的抗压强度,其导热系数随温度和密度的升高而增大,泡沫材料在深冷情况下表现出优异的绝热性能．同时对酚醛泡沫材料的燃烧性能进行了考察,其临界氧指数高达４７,在高于１５０℃环境温度中有自燃的危险,１５０℃以下可安全使用．     

免疫沉淀法分离纯化感染细胞中的甲肝病毒RNA

本研究采用抗血清（多抗血清）沉淀甲肝病毒,并用盐酸胍酸性酚,氯仿一步法分离纯化病毒ＲＮＡ．此方法能排除非病毒ＲＮＡ的污染,操作简单,要求条件较低,ＲＮＡ的纯度和完整性都较好     

泛光照明效果的计算机模拟

从实际灯具的配光曲线及被照面材料的反射特性入手,运用光度学和色度学的计算方法,详细介绍了泛光照明效果的计算机模拟程序的设计思想和分析方法,按照这一思想设计的软件在泛光照明设计中将十分有用。