Stability of Methods for Matrix Inversion

Inversion of a triangular matrix can be accomplished in severalways. The standard methods are characterized by the loop ordering,whether matrix-vector multiplication, solution of a triangularsystem, or a rank-1 update is done inside the outer loop, andwhether the method is blocked or unblocked. The numerical stabilityproperties of these methods are investigated. It is shown thatunblocked methods satisfy pleasing bounds on the left or rightresidual. However, for one of the block methods it is necessaryto convert a matrix multiplication into the solution of a multipleright-hand side triangular system in order to have an acceptableresidual bound. The inversion of a full matrix given a factorizationPA=LU is also considered, including the special cases of symmetricindefinite and symmetric positive definite matrices. Three popularmethods are shown to possess satisfactory residual bounds, subjectto a certain requirement on the implementation, and an attractivenew method is described. This work was motivated by the questionof what inversion methods should be used in LAPACK.     

冀东金矿集中区控矿条件探讨

论述了冀东金矿集中区绿岩型金矿的矿质来源，并恢复其矿源层的原岩。对构造及中小型岩浆任入体的控矿作用作了论述，并提出了成矿模式。     

On the sensitivity of the LU factorization

This paper gives sensitivity analyses by two approaches forL andU in the factorizationA=LU for general perturbations inA which are sufficiently small in norm. By the matrix-vector equation approach, we derive the condition numbers for theL andU factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting affect the sensitivity of the LU factorization. The material presented here is a part of the first author's PhD thesis under the supervision of the second author. This research was supported by NSERC of Canada Grant OGP0009236.     

Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces

Summary Some stability and convergence theorems of the modified Ishikawa iterative sequences with errors for asymptotically nonexpansive mapping in the intermediate sense and asymptotically pseudo contractive and uniformly Lipschitzian mappings in Banach spaces are obtained.     

基于3S技术的土地利用动态变化研究

3S技术是研究土地利用动态变化的重要技术手段，具有传统方法无法比拟的优越性。本文以秦皇岛市为例，定量分析了区域内土地利用动态变化。针对区域土地利用程度及生态环境可能产生的影响进行了简要的评价，揭示了研究区土地利用变化规律，为秦皇岛市实现生态环境目标提供决策依据。     

对"晨光"体育活动的审度与思考

在总结河南省“晨光”体育活动成功经验的基础上 ,对提高学校体育的水平与质量进行了理论性论证 ,进而提出了“晨光”体育活动应推广与普及的合理化建议及可行性措施 .     

一种简易新型长光程薄层光谱电化学池

设计并制作了一种新型长光程薄层光谱电化学池，其具有光程长、灵敏度高、重现性好等特点，且组装简便，电极容易更换，溶液未补偿电阻小，溶液用量少．易清洗．电解池以石墨为工作电极，分别用循环伏安、交流阻抗技术、光谱恒电位技术对其性能进行测试，得到比较满意的结果．     

Perfect information two-person zero-sum markov games with imprecise transition probabilities

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.     

关于拟AP内射模的一些研究

Let R be a ring. R is called right AP-injective if, for any a ∈ R, there exists a left ideal of R such that lr(a) = Ra (?) Xa. We extend this notion to modules. A right .R-module M with 5 = End(MR) is called quasi AP-injective if, for any s ∈ S, there exists a left ideal Xs of S such that ls(Ker(s)) = Ss (?) Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.     

Design and Fabrication of 1.06 μm Resonant-Cavity Enhanced Reflective Modulator with GaInAs/GaAs Quantum Wells

A resonant-cavity enhanced reflective optical modulator is designed and fabricated, with three groups of three highly strained InGaAs/GaAs quantum wells in the cavity, for low voltage and high contrast ratio operation. The quantum wells are positioned in antinodes of the optical standing wave. The modulator is grown in a single growth step in an molecular beam epitaxy system, using GaAs/AlAs distributed Bragg reflectors as both the top and bottom mirrors. Results show that the reflection device has a modulation extinction of 3 dB at -4.5 V bias.