The Role of Arithmetic in Fast Parallel Matrix Inversion

In the last two decades several NC algorithms for solving basic linear algebraic problems have appeared in the literature. This interest was clearly motivated by the emergence of a parallel computing technology and by the wide applicability of matrix computations. The traditionally adopted computation model, however, ignores the arithmetic aspects of the applications, and no analysis is currently available demonstrating the concrete feasibility of many of the known fast methods. In this paper we give strong evidence to the contrary, on the sole basis of the issue of robustness, indicating that some theoretically brilliant solutions fail the severe test of the ``Engineering of Algorithms.' We perform a comparative analysis of several well-known numerical matrix inversion algorithms under both fixed- and variable-precision models of arithmetic. We show that, for most methods investigated, a typical input leads to poor numerical performance, and that in the exact-arithmetic setting no benefit derives from conditions usually deemed favorable in standard scientific computing. Under these circumstances, the only algorithm admitting sufficiently accurate NC implementations is Newton's iterative method, and the word size required to guarantee worst-case correctness appears to be the critical complexity measure. Our analysis also accounts for the observed instability of the considered superfast methods when implemented with the same floating-point arithmetic that is perfectly adequate for the fixed-precision approach. Received March 28, 1998; revised February 2, 1999, and April 21, 1999.     

基于VC++复数模板实现一般复矩阵的奇异值分解运算

Ｖｉｓｕａｌ　Ｃ＋＋以其方便的可视化集成编程环境,高效的代码实现功能,强大的基内库以及兼有低级语言可控制硬件操作的优点,成为一般工程项目的首选软件开发平台。涉及信号处理的实际工程常常需要处理复的数字信号,因此Ｖｉｓｕａｌ　Ｃ＋＋下如何实现复数运算是工程技术中软件开发必须面对的问题。该文详细阐述了ＶｉｓｕａｌＣ＋＋中利用复数模板实现复数运算的方法,给出了一些基本复数运算的实现代码;并基于该方法实现了算法已知的一般复矩阵的奇异值分解（ＣＳＶＤ）运算,很好地满足了实际工程信号处理软件模块的需要,证明了该方法的正确性。发现了 Ｖｉｓｕａｌ　Ｃ＋＋５．０和Ｖｉｓｕａｌ　Ｃ＋＋６．０一个声明的复数模板函数在其标准Ｃ＋＋库中没有具体实现,通过编写同名模板函数解决了这一问题。     

Further remarks for the matrix type-B codes

Different philosophies lie behind the detecting and correcting error patterns in a real communication channel. The sceptic points in choosing an efficient code, specifically the matrix type-B code, were pointed out in Refs. 1 and 2.Some more points are shown here. As a result the matrix type-B code is found to be a best choice. Some more theoretical aspects for this code are also given. These are useful for the realization and testing of an encoding-decoding algorithm with IC's used in a unique way for its implementation.     

空间3-UPU/UPU机构的刚度分析

以3-UPU/UPU并联机构为例,进行机构分析及运动学分析,得到机构的雅克比矩阵;在静平衡条件下计算出并联机构的局部刚度矩阵和全局刚度矩阵;利用数学软件MATLAB绘制3-UPU/UPU并联机构的局部刚度曲线以及全局刚度曲线,分析上下平面外接圆半径的变化对局部刚度和全局刚度的影响.结果表明局部刚度矩阵以及全局刚度取决于机构的位姿,对于给定的位姿可求机构局部刚度及全局刚度的变化范围;机构的上下表面半径的变化情况影响着局部刚度和全局刚度,因此可以适当地增大上下表面半径来获得较高的局部刚度以及全局刚度。     

钢筋混凝土梁的优化设计

针对钢筋混凝土结构承载力和工程造价要求,采用罚函数法,对钢筋混凝土梁的截面尺寸和钢筋的用量进行优化设计.提出了采用矩阵实验室(MATLAB)优化工具箱的方法,对C20到C40混凝土和HRB335,HRB400钢筋进行多种组合.结果显示在满足承载力要求及规范所规定的构造要求条件下,选用C35和HRB400为最经济的设计方案.     

Pseudo-transient continuation-based variable relaxation solver in nonlinear magnetohydrodynamic simulations

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first- and/or second-order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray X1E. Two schemes are derived in this work, first- and second-order variable relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; next the system is carefully initialized by the solution with linear conductivity; third, time step and relaxation factor are vertex-based varied and optimized at each time step; finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.     

隐蔽流树方法的分析与改进

利用隐蔽流树方法搜索隐蔽通道时,获得的操作序列中只有极少部分真正构成隐蔽通道,增加了后续手工分析的工作量。为此,提出一种改进的隐蔽流树方法。根据信息流图进行建树,设计信息流规则,并给出隐蔽流树的自动分析算法。以一个文件系统为例进行分析,结果验证了改进方法的正确性。