A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems

In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be indefinite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton-Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method to solve the generalized algebraic Lyapunov equation (GALE) appearing in the Kleinman algorithm is given.     

Bernstein型多项式线性组合的点态逼近

引进Berstein型多项式的线性组合算子，研究其点态逼近的速度和逆定理，刻画了它的其逼近特征。     

Fuzzy集的表现定理

本文利用集合套的理论，基于Ｆｕｚｚｙ集的交分解，推导出了数“乘”经典集的交形式下表现定量的新形式，从而对研究Ｆｕｚｚｙ系统的代数性质带来一些方便。     

关于Bernstein－Durrmeyer算子的注记

研究Ｂｅｒｎｓｔｅｉｎ－Ｄｕｒｒｅｙｅｒ算子Ｍｎ（ｆ，ｘ），给出正逆定理和导数的特征刻划定理。     

阿贝尔方法及其在无穷级数中的应用

本文简略地介绍阿贝尔（Ｎｉｅｌｓ Ｈｅｎｒｉｋ Ａｂｅｌ，１８０２－１８２９）在数学方面的成就及阿贝尔方法，把对级数＋∞∑ｎ＝０ａｎＶｎ收敛性的几个判别定理的证明统一在阿贝尔方法之下，拓宽了它们的适用范围。     

On quantization,truncation and jitter errors in the sampling theorem and its generalizations

Any band-limited signal f(t) can, according to the sampling theorem, be exactly reconstructed from its sampled values. If the signal is not necessarily band-limited, an alternative model states that it can be approximately reconstructed from its samples. Such signals can also be approximated by generalized sampling sums which can be interpreted as discretized convolution integrals of Fejér's type. In all three cases the physically realized signal is often only roughly equal to f(t) due to errors caused e.g. by the sampling mechanism.In this paper the following types of errors are treated: (1) round-off error arising when quantized sampled values are used, (2) truncation error, arising when a truncated sum is used for representation, (3) time jitter error, a result of sampling at instants slightly different from the sample values. All proofs employ deterministic methods.     

Discrete linear Hamiltonian eigenvalue problems

This paper introduces general discrete linear Hamiltonian eigenvalue problems and characterizes the eigenvalues. Assumptions are given, among them the new notion of strict controllability of a discrete system, that imply isolatedness and lower boundedness of the eigenvalues. Due to the quite general assumptions, discrete Sturm-Liouville eigenvalue problems of higher order are included in the presented theory.     

信道最优的变换编码--联合信源信道编码的一种新方法

简要介绍Shannon分离理论的优缺点，并由此引入对联合信源信道编码的介绍，重点对联合信源信道编码方法中的信道最优的变换编码方法进行了论述，同时也对信道最优的变换编码的设计及其性能进行了介绍。