.基于用户查询扩展的自动摘要技术*

提出了一种新的文档自动摘要方法,利用非负矩阵分解算法将原始文档表示为若干语义特征向量的线性组合,通过相似性计算来确定与用户查询高度相关的语义特征向量,抽取在该向量上具有较大投影系数的句子作为摘要,在此过程中,多次采用相关反馈技术对用户查询进行扩展优化。实验表明,该方法所得摘要在突出文档主题的同时,体现了用户的需求和兴趣,有效改善了信息检索的效率。     

An Estimation of Complexity and Computational Costs for Vertical Block-Cyclic Distributed Parallel LU Factorization

The Vertical Block–cyclic Distributed Parallel LU Factorization Method (VBPLU) is effectively processed on a distributed memory parallel computer. VBPLU is based on the two techniques, the block algorithm and the aggregation of communications. Since startup time dominates the data communication and the aggregation reduces communication isssues, the total performance has been much improved. Furthermore this method uses long vectors so that it is also advantageous on vector processors. In this paper, we have constructed a modeling of VBPLU using a simplified LogGP model with analytical formulae, and estimated accurately the computational cost taking into account load distributions caused by data layout and process mapping. Some knowledge for optimization of block algorithm has been obtained. Our estimations have been verified through numerical experiments on three different distributed memory parallel computers.     

Sparse least squares support vector training in the reduced empirical feature space

In this paper we discuss sparse least squares support vector machines (sparse LS SVMs) trained in the empirical feature space, which is spanned by the mapped training data. First, we show that the kernel associated with the empirical feature space gives the same value with that of the kernel associated with the feature space if one of the arguments of the kernels is mapped into the empirical feature space by the mapping function associated with the feature space. Using this fact, we show that training and testing of kernel-based methods can be done in the empirical feature space and that training of LS SVMs in the empirical feature space results in solving a set of linear equations. We then derive the sparse LS SVMs restricting the linearly independent training data in the empirical feature space by the Cholesky factorization. Support vectors correspond to the selected training data and they do not change even if the value of the margin parameter is changed. Thus for linear kernels, the number of support vectors is the number of input variables at most. By computer experiments we show that we can reduce the number of support vectors without deteriorating the generalization ability.

Discrete J-spectral factorization

This paper deals with the J-spectral factorization for general discrete rational matrices. A simple approach based on the Kalman filtering in Krein space is proposed. The main idea is to construct a stochastic state space filtering model in Krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized. The spectral factor is then easily derived by using the generalized Kalman filtering in Krein space, which is similar to the H₂ spectral factorization. Our approach unifies the treatment of the H₂ spectral factorization and the J-spectral factorization. The applications of the derived results in H_∞ and risk-sensitive estimation for both nonsingular and singular systems are demonstrated.     

关于酉对称矩阵的QR分解的注记

研究了行(列)酉对称矩阵的性质,修正了行(列)酉对称矩阵的QR分解的公式和快速算法.结果可减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.     

On sparse lu factorization procedures for the solution of parabolic differential equations in three space dimensions

The numerical solution of partial differential equations in 3 dimensions by finite difference methods leads to the problem of solving large order sparse structured linear systems.

In this paper, a factorization procedure in algorithmic form is derived yielding direct and iterative methods of solution of some interesting boundary value problems in physics and engineering.     

Computation of eigenvalues of a real matrix

This paper presents a computational procedure for finding eigenvalues of a real matrix based on Alternate Quadrant Interlocking Factorization, a parallel direct method developed by Rao in 1994 for the solution of the general linear system Ax=b. The computational procedure is similar to LR algorithm as studied by Rutishauser in 1958 for finding eigenvalues of a general matrix. After a series of transformations the eigenvalues are obtained from simple 2×2 matrices derived from the main and cross diagonals of the limit matrix. A sufficient condition for the convergence of the computational procedure is proved. Numerical examples are given to demonstrate the method.