回归曲线的加权正交级数估计

回归曲线的加权正交级数估计杨瑛（北京大学概率统计系，北京１００８７１）国家自然科学基金资助项目．１９８９年１２月３日收到．１９９０年１１月２２日收到第一次修改稿．１９９２年８月７日收到第二次修改稿．一、引论自１９６２年Ｃｅｎｃｏｖ［１］提出了密度函数...     

一类三次系统的定性分析

一类三次系统的定性分析陈文灯（中央财政金融学院信息系，北京１０００８１）国家自然科学基金资助项目．１９９２年６月５日收到．１９９３年６月１６日收到修改稿．本文对一类三次系统进行了定性分析，得出系统（１）的极限环的存在性、唯一性及不存在性的条件．定理１...     

论多目标分式规划

论多目标分式规划徐增堃（浙江师范大学数学系，金华３２１００４）基金项目：浙江省教委自然科学基金资助课题．１９９０年１０月２９日收到，１９９１年１０月５日收到第一次修改稿．１９９２年９月７日收到第二次修改稿，１９９３年２月１３日收到第三次修改、压缩稿．...     

一类互惠共存系统的定态分歧与稳定性

一类互惠共存系统的定态分歧与稳定性李大华，傅一平（华中理工大学数学系，武汉４３００７４）基金项目：国家自然科学基金资助项目．１）现在江西省九江师范专科学校工作，邮政编码３３２０００．１９９２年５月６日收到．一、引言在文［１］中Ｒ．Ｍ．Ｍａｙ提出了一个...     

截断族中参数与半参数估计

截断族中参数与半参数估计陈桂景（安徽大学，合肥２３００３９）赵忠柏（吉林工业大学，长春１３００２５）丁元耀（安徽大学，合肥２３００３９）基金项目：国家自然科学基金资助项目１９９１年１月９日收到，１９９２年７月１３日收到第一次修改稿，１９９３年毛月１３...     

具有无界时滞的微分方程解的振动性

具有无界时滞的微分方程解的振动性刘正荣（云南大学数学系和云南省应用数学研究所，昆明６５００９１）俞元洪（中国科学院应用数学研究所，北京１０００８０）基金项目：国家自然科学基金资助项目１９９２年３月２５日收到．一、引言考虑泛函微分方程ｉ＝１其中，．关于...     

实轴上Freud-Fourier级数的平均收敛性

实轴上Ｆｒｅｕｄ－Ｆｏｕｒｉｅｒ级数的平均收敛性闵国华，肖资阳（南京理工大学应用数学系，南京２１００１４）１９９１年２月４日收到１９９２年２月１０日收到修改压缩稿．一、引言记Ｈｅｒｍｉｔｅ权函数，Ｓｎ（ｘ）为ｆ（ｘ）的Ｈｅｒｍｉｔｅ级数的前１项和．关...     

可压核废料污染问题的数值方法

可压核废料污染问题的数值方法李潜（山东大学数学系，济南２５０１００）国家自然科学基金资助项目．１９９１年１１月４日收到，１９９２年６月１６日收到修改压缩船．一、引言多孔介质中，可压缩核废料污染问题的数学模型是下述抛物型方程组的初边值问题［１］其中ｐ是...     

求解粘性系数的迭代方法及其收敛性

求解粘性系数的迭代方法及其收敛性丛文相（黑龙江大学，哈尔滨１５００８０）１９９１年８月３０日收到．１９９２年８月２５日收到第一次修改稿．１９９２年１２月４日收到第二次修改稿．一、引言研究地震正、反问题时，一般把地球假设为完全弹性体，而实际地球介质并非...     

非等谱Lax算子族的Virasoro代数

非等谱Ｌａｘ算子族的Ｖｉｒａｓｏｒｏ代数马文秀（复旦大学数学研究所，上海２００４３３）国家博士后科学基金资助项目．１９９１年７月２５日收到．１９９２年７月６日收到修改稿．一、引言Ｌａｘ算子方法［１］在可积系统理论中有着广泛的应用．从一个谱问题出发我们...     

Some New Perturbation Bounds for the Generalized Polar Decomposition

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented.     

A Note on the Perturbation Bound of <Emphasis Type="Italic">Q</Emphasis>-factors

In this note we present a perturbation bound of unitary polar factors.We add the orthogonalprojectors into the bound;as a result,a uniform perturbation bound of Q-factors is obtained,and the previousbounds are improved.     

Remarks on virtual bound states for semi—bounded operators

We calculate the number of bound states appearing below the spectrum of a semi—bounded operator in the case of a weak, indefinite perturbation. The abstract result generalizes the Birman—Schwinger principle to this case. We discuss a number of examples, in particular higher order differential operators, critical Schrodinger operators, systems of second order differential operators, Schrodinger type operators with magnetic fields and the Two—dimensional Pauli operator with a localized magnetic field.     

THE STRUCTURE SENSITIVITY ANALYSIS FOR TRIANGULAR SYSTEMS

Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.     

On computation of the steady-state probability distribution of probabilistic Boolean networks with gene perturbation

Given a Probabilistic Boolean Network (PBN), an important problem is to study its steady-state probability distribution for network analysis. In this paper, we present a new perturbation bound of the steady-state probability distribution of PBNs with gene perturbation. The main contribution of our results is that this new bound is established without additional condition required by the existing method. The other contribution of this paper is to propose a fast algorithm based on the special structure of a transition probability matrix of PBNs with gene perturbation to compute its steady-state probability distribution. Experimental results are given to demonstrate the effectiveness of the new bound, and the efficiency of the proposed method.     

群逆的扰动界及其在奇异线性系统中的应用

本文建立了群逆的扰动界,此界基于矩阵A的Jordan标准形和P-范数,其中P是非异矩阵满足 是非异上双对角阵且 当矩阵A和A+E有相同的秩且 较小时,得到了 较好的估计.在相同的条件下,研究了相容的奇异线性系统Aχ=b的扰动,给出了χopt=A#b扰动的上界,其中A#是A的群逆,χopt是最小P-范数解.     

A PERTURBATION ANALYSIS FOR THE PROJECTION OF A STIFFLY SCALED MATRIX

In this paper we study the perturbation bound of the projection (WA )(WA ), where both the matrices A and W are given with W positive diagonal and severely stiff. When the perturbed matrix A=A δA satisfy several row rank preserving conditions, we derive a new perturbation bound of the projection.     

Estimation of optimal backward perturbation bounds for the linear least squares problem

In this paper a method of estimating the optimal backward perturbation bound for the linear least squares problem is presented. In contrast with the optimal bound, which requires a singular value decomposition, this method is better suited for practical use on large problems since it requiresO(mn) operations. The method presented involves the computation of a strict lower bound for the spectral norm and a strict upper bound for the Frobenius norm which gives a gap in which the optimal bounds for the spectral and the Frobenius norm must be. Numerical tests are performed showing that this method produces an efficient estimate of the optimal backward perturbation bound.     

Accuracy and Stability of the Null Space Method for Solving the Equality Constrained Least Squares Problem

The null space method is a standard method for solving the linear least squares problem subject to equality constraints (the LSE problem). We show that three variants of the method, including one used in LAPACK that is based on the generalized QR factorization, are numerically stable. We derive two perturbation bounds for the LSE problem: one of standard form that is not attainable, and a bound that yields the condition number of the LSE problem to within a small constant factor. By combining the backward error analysis and perturbation bounds we derive an approximate forward error bound suitable for practical computation. Numerical experiments are given to illustrate the sharpness of this bound.     

一类时变非线性系统的一致有界性的注记

主要研究带干扰的广义齐次系统的一致有界和一致最终有界性 ,证明了当干扰项满足一致有界及Lp 可积时系统的一致有界性及一致最终有界性 ,本质推广了最近相关文献中的有关系统一致有界性的结果 .