数值鲁棒的非线性滤波新方法

应用多维情形的二阶插值公式构造新型非线性滤波器。该滤波器不需非线性函数的偏导计算，便能代替常规的扩展卡尔曼滤波器，并有滤波精度高、数值计算稳定和适用范围宽等优点。仿真实例表明新滤波器具有较高的性能。     

Designing robustly stabilising controllers for LTI spatially distributed systems using coprime factor synthesis

This paper considers the design of feedback controllers for linear, time-invariant, spatially distributed systems in an approach which generalises the H^∞-framework and in particular the H^∞ loop-shaping method. To this end, we introduce a class of spatially distributed system models called finite dimensional, distributed, linear, time-invariant systems. Sensors and actuators are considered to be part of the controller, rather than part of the plant, and thus the controller we wish to design is itself a spatially distributed system. Optimising over placements and shapes of the sensor and actuator spatial distribution functions is an integrated part of the controller design procedure. As an illustrative design example, we present the feedback stabilisation of an electrostatically destabilised, electrically conducting membrane.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

Finding Optimal Ordering of Sparse Matrices for Column-Oriented Parallel Cholesky Factorization

In this paper, we consider the problem of finding fill-preserving sparse matrix orderings for parallel factorization. That is, given a large sparse symmetric and positive definite matrix A that has been ordered by some fill-reducing ordering, we want to determine a reordering that is appropriate in terms of preserving the sparsity and minimizing the cost to perform the Cholesky factorization in parallel. Past researches on this problem all are based on the elimination tree model, in which each node represents the task for factoring a column, and thus, can be seen as a coarse-grained task dependence model. To exploit more parallelism, Joseph Liu proposed a medium-grained task model, called the column task graph, and showed that it is amenable to the shared-memory supercomputers. Based on the column task graph, we devise a greedy reordering algorithm, and show that our algorithm can find the optimal ordering among the class of all fill-preserving orderings of the given sparse matrix A.     

大数质因子分解的量子算法

量子质因子分解算法是一种利用波的特性在量子环境下进行整数质因子分解的新方法。本文首先介绍了量子质因子分解的基本思想及其相关概念，然后分析并给了了大数质因子分解的量子算法，最后对量子算法的发展前景进行了展望。     

一种快速分解大整数的小因子的优化分解树OFT算法

分解大整数的小因子是解决IFP，DLP问题的诸多攻击方法中的重要运算模块．本文在目前分解大整数小因子算法的基础上，提出的优化分解树(Optimized Factorization Tree)算法，利用树型数据结构和相应的构造算法与回溯算法，配合以作者提出的分解表截支方法和优化分组策略，可以将分解大整数小因子的速度提高50％以上．该算法还可以为大整数素性判别做高效过滤，快速识别大部分合数．     

同时镇定问题研究

基于互质分解的状态空间描述，首先得到了可同阶强镇定的充要条件，并给出了一种同阶强定控制器的构造方法，本文证明了２对象同时强镇定可转化为同时强镇定－辅助对象与它的子对象，同阶同时强全２对象等价于同时强镇定一个辅助对象与它的一稳定子对象，同时镇定ｒ＋１个对象等价同时强镇定ｒ－１辅助对象它们的一公共子对象。     

具有完整性的状态反馈H2最优控制器设计

基于互质分解的状态空间描述方法,给出了状态反馈下对执行器失效具有完整性的 H2最优控制器的一种新的参数化形式,将具有完整性H2最优控制器设计转化为设计一严格 正则的稳定控制器同时镇定对应于k个故障状态的k个辅助对象.     

LU分解递归算法的研究

将递归方法引入稠密线性代数的计算，能产生自动的矩阵分块，使算法适合于当今分级存储高性能计算机的结构，提高运算速度。文中对解线性代数方程组的LU分解递归算法进行了研究，给出了算法的详细推导过程。     

Algebraic Riccati equation and J-spectral factorization for estimation

In this paper we investigate on the existence of the stabilizing solution of the algebraic Riccati equation (ARE) related to the filtering problem with a prescribed attenuation level γ. It is well known that such a solution exists and is positive definite for γ larger than a certain γ_F and it does not exist for γ smaller than a certain γ₀. We consider the intermediate case γ(γ₀,γ_F] and show that in this interval the stabilizing solution does exist, except for a finite number of values of γ. We show how the solution of the ARE may be employed to obtain a minimum-phase J-spectral factor of the J-spectrum associated with the filtering problem.