Cholesky分解递归算法与改进

递归算法是计算稠密线性代数的一种新的有效方法。递归产生自动、变化的矩阵分块,能充分发挥当今分级存储高性能计算机的效率。对Cholesky分解递归算法进行了研究,给出了算法的详细推导过程,用具有递归功能的Fortran90实现了算法,并通过矩阵元素顺序重排的方法,进一步提高了递归算法的运算速度。研究产生的算法比目前常用的分块算法快15％－25％。     

乔莱斯基分解递归算法的研究

1 引言以乔莱斯基(Cholesky)分解、LU分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用。随着计算机结构和技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展。通用的基本线性代数子程序库BLAS(Basic Lin-ear Algebra Subprograms)从70年代的Level-1 BLAS(执行向量一向量运算),发展到80年代的Level-2     

基于LDLT分解求实对称矩阵特征值的递归算法

基于线性代数与矩阵理论,给出利用LDLT分解计算实对称矩阵特征值的递归算法。该算法可求出实对称矩阵在给定区间内的特征值的个数,并可计算满足精度要求的特征值。理论分析和实际测试证明该算法是有效的。     

LU分解递归算法的实现

§1.引言 以LU分解, Cholesky分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用.随着计算机技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展.目前,具有多级存储结构的高性能RISC计算机已占据了数值计算领域的主导地位. RSIC处理器的运算速度非常快,它们与存储器之间的速度差距很大.计算机的性能能不能充分发挥,多级存储结构与高缓能否得到有效利用成为关键.为此,现行的     

矩阵的Doolittle递归分解算法及符号程序设计

将矩阵An×n的Doolittle分解推广到Am×n上，并在常规的迭代算法上加以创新，给出了递归的分解算法．在实现算法的过程中，对数据进行了巧妙处理，使中间数据及最终计算结果都具有分数形式，提高了结果的精确度，而且更符合人们阅读的习惯．经过运行测试，算法设计合理，程序运行高效准确．程序是对MathSoft公司的交互式的数学文字软件Mathcad的矩阵分解的数值计算扩充到符号运算．     

Smith图导出关系模式的分解算法与递归处理

本文提出了一种由优化的Ｓｍｉｔｈ图导出规范化关系模式的分解算法,包括确定根结点、,生成森林、导出规范化、关系模式等。这些都是用递归处理实现的,本文给出了这些递归处理的描述,最后介绍了一个例子。     

递归的非递归算法研究

本文对递归的非递归算法进行了研究，并给出了由递归到递推的抽象算法，并说明了该算法的具体运用。     

基于递归分解的因果结构学习算法

在高维小样本场景下,针对现有基于约束的因果结构学习方法存在因果结构学习效率低、马尔可夫等价类的问题,以非线性非高斯的高维小样本为研究对象,提出一种基于递归分解的因果结构学习算法CADR。在高维小样本的因果结构学习效率方面,结合递归分解的思想,将高维变量集递归分解为多个更小的子集,直到无法再分解或子集的大小达到阈值为止。在该过程中,变量集的减少缩减了条件独立性检验的条件候选集的搜索空间,从而提高学习效率。同时,为进一步识别马尔可夫等价类,根据非线性非高斯模型的因果方向的不可逆性,通过判断拟合噪声项与原因变量是否独立来识别马尔可夫等价类的因果方向。在仿真数据和真实因果结构数据上的实验结果表明,CADR不仅提高条件独立性检验的效率,而且能有效地区分马尔可夫等价类,学习到更精确的因果结构,其中,在真实因果结构实验中,与现有Xie＿rec、PC＿ANM和Notear＿Sob方法相比,F1评分提高5%～12%。     

一种新的基于递归分解的图可达性查询算法

针对现实中许多超大规模图可达性查询的问题,提出了一种新的基于递归分解的算法,即将原图递归分解成一系列生成树和剩余图两类子图,并通过分别查询这两类子图来减少查询开销.相比于区间标记、链分解、2-hop标签和路径树等传统算法,该算法不仅空间开销更小,且时间复杂度更低.仿真实验表明,该算法对处理大规模有向图可达性问题上存储规模更小且查询效率更高.     

一种LU分解与迭代法的结构策略及算法实现

在矩阵求解算法，直接法或迭代法都能．有效地求解大规模稀疏或病态矩阵，因此提出一种LU分解与迭代法结合的策略，采用LU分解对矩阵进行预处理，以提高迭代法的收敛性，并采用一种判断策略使矩阵的LU分解结果可最限度地重复利用，些结合策略应用于两种共轭梯度（CG）法，得到CLUCG和CLUTCG两种算法。它们已应用于模拟和混合信号电路模拟器ZeniVDE中，大量实验结果表明此结合策略是很有效的，得到的两种算法具有较好的速度和较好的收敛性。     

MDA加密算法的应用及其算法分析与改进

提出了一种新的MDA置乱信息加密方法。结合递归运算,设计了基于MDA置换的信息加密、解密算法。首先由随机函数生成得到任意的不相等的混沌序列,以此序列作镜像变换后对信息进行置换而得到加密文件。解密算法是加密算法的逆过程。实验结果表明,该算法能够得到令人满意的结果。     

关于矩阵最优路径算法的探讨

本文讨论了矩阵最优路径的串行和并行算法。在串行方面讨论了用动态规划思想的求解算法;在并行方面给出了计算模型。并给出算法描述和算法复杂性分析。     

引入偏置的矩阵分解推荐算法研究

由于矩阵分解良好的可扩展性和较高的预测精度,在推荐算法的应用中都有出色的表现。本文在基础的矩阵分解模型上先后加入全局偏置和时间偏置,以提高预测准确度和推荐质量。以个性化推荐系统为对象,在MovieLens数据集上的实验表明,两种方法在一定程度上提高了算法的准确度。     

Optimizing the parallel computation of linear recurrences using compact matrix representations

This paper presents a novel method for optimizing the parallel computation of linear recurrences. Our method can help reduce the resource requirements for both memory and computation. A unique feature of our technique is its formulation of linear recurrences as matrix computations, before exploiting their mathematical properties for more compact representations. Based on a general notion of closure for matrix multiplication, we present two classes of matrices that have compact representations. These classes are permutation matrices and matrices whose elements are linearly related to each other. To validate the proposed method, we experiment with solving recurrences whose matrices have compact representations using CUDA on nVidia GeForce 8800 GTX GPU. The advantages of our technique are that it enables the computation of larger recurrences in parallel and it provides good speedups of up to eleven times over the un-optimized parallel computations. Also, the memory usage can be as much as nine times lower than that of the un-optimized parallel computations. Our result confirms a promising approach for the adoption of more advanced parallelization techniques.     

Weighted archetypal analysis of the multi-element graph for query-focused multi-document summarization

Most existing research on applying the matrix factorization approaches to query-focused multi-document summarization (Q-MDS) explores either soft/hard clustering or low rank approximation methods. We employ a different kind of matrix factorization method, namely weighted archetypal analysis (wAA) to Q-MDS. In query-focused summarization, given a graph representation of a set of sentences weighted by similarity to the given query, positively and/or negatively salient sentences are values on the weighted data set boundary. We choose to use wAA to compute these extreme values, archetypes, and hence to estimate the importance of sentences in target documents set. We investigate the impact of using the multi-element graph model for query focused summarization via wAA. We conducted experiments on the data of document understanding conference (DUC) 2005 and 2006. Experimental results evidence the improvement of the proposed approach over other closely related methods and many of state-of-the-art systems.     

Scientific articles recommendation with topic regression and relational matrix factorization

In this paper we study the problem of recommending scientific articles to users in an online community with a new perspective of considering topic regression modeling and articles relational structure analysis simultaneously. First, we present a novel topic regression model, the topic regression matrix factorization （tr-MF）, to solve the problem. The main idea of tr-MF lies in extending the matrix factorization with a probabilistic topic modeling. In particular, tr-MF introduces a regression model to regularize user factors through probabilistic topic modeling under the basic hypothesis that users share similar preferences if they rate similar sets of items. Consequently, tr-MF provides interpretable latent factors for users and items, and makes accurate predictions for community users. To incorporate the relational structure into the framework of tr-MF, we introduce relational matrix factorization. Through combining tr-MF with the relational matrix femtorization, we propose the topic regression collective matrix factorization （tr-CMF） model. In addition, we also present the collaborative topic regression model with relational matrix factorization （CTR-RMF） model, which combines the existing collaborative topic regression （CTR） model and relational matrix factorization （RMF）. From this point of view, CTR-RMF can be considered as an appropriate baseline for tr-CMF. Further, we demonstrate the efficacy of the proposed models on a large subset of the data from CiteULike, a bibliography sharing service dataset. The proposed models outperform the state-of-the-art matrix factorization models with a significant margin. Specifically, the proposed models are effective in making predictions for users with only few ratings or even no ratings, and support tasks that are specific to a certain field, neither of which has been addressed in the existing literature.