基于矩阵完整化的分块整合推荐算法

传统的推荐系统往往是通过使用协同过滤或基于内容的方式来实现的,而文中将矩阵完整化的方法应用到推荐系统中。由于数据的稀疏性,直接使用矩阵完整化的方法会给推荐结果带来不小的误差。考虑到使用用户中存在一些活跃用户,挖掘出这些特殊用户,由他们组成的数据会降低稀疏性,而且对活跃用户提高 推荐质量,会产生更大的商业价值。提出了一种分块整合推荐的方法,实验结果表明该方法能够提升推荐精度。     

Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants

Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.     

Dynamic normal forms and dynamic characteristic polynomial

We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case, our algorithm supports rank-one updates in O(n²logn) randomized time and queries in constant time, whereas in the general case the algorithm works in O(n²klogn) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on the first dynamic algorithm for computing normal forms of a matrix such as the Frobenius normal form or the tridiagonal symmetric form. The algorithm can be extended to solve the matrix eigenproblem with relative error 2^−b in additional O(nlog²nlogb) time. Furthermore, it can be used to dynamically maintain the singular value decomposition (SVD) of a generic matrix. Together with the algorithm, the hardness of the problem is studied. For the symmetric case, we present an Ω(n²) lower bound for rank-one updates and an Ω(n) lower bound for element updates.     

A Proof-Planning Framework with explicit Abstractions based on Indexed Formulas

A major motivation of proof-planning is to bridge the gap between high-level, cognitively adequate reasoning for specific domains, and calculus-level reasoning to ensure soundness. For high reasoning levels the cognitive adequacy of representation and reasoning techniques is a major issue, while for lower reasoning levels the adequacy wrt. the modelled domain is important. Furthermore, proof construction is an engineering task and there is a need to support the design and application of proof-search engineering methods. To this end we present a framework to explicitly support different reasoning levels. To structure reasoning levels the framework allows for an explicit representation of abstractions and proof-search refinement techniques. In order to ensure soundness within a reasoning level, we use techniques developed in the context of matrix characterisation relying on the notion of indexed formulas. Furthermore, we introduce a uniform concept for contextual reasoning, and sketch basic tacticals for the definition of tactics to organise the overall proof-search inside and across different reasoning levels.     

Efficient Solution of A, x ( k )?= b ( k ) Using A ?1

In this work, we consider the problem of solving , , where b ^(k+1) = f(x ^(k)). We show that when A is a full matrix and , where depends on the specific software and hardware setup, it is faster to solve for by explicitly evaluating the inverse matrix A ⁻¹ rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.     

三维图形引擎中骨骼蒙皮动画的一种实现方法*

提出了三维图形引擎中骨骼蒙皮动画的一种实现方法,即将现有的关节动画与单一网格动画相结合,利用骨架的继承变换和顶点混合技术使骨骼蒙皮动画平滑逼真。实验表明该方法有良好的显示效果,并具有较好的实时性,且占用的存储空间不大,能够满足当前三维图形引擎对动画技术的要求。     

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.