This paper establishes an improvement on the QL algorithm for a symmetric tridiagonal matrix T so that we can work out the eigenvalues of T faster. Meanwhile, the new algorithm don’t worsen the stability and precisio...This paper establishes an improvement on the QL algorithm for a symmetric tridiagonal matrix T so that we can work out the eigenvalues of T faster. Meanwhile, the new algorithm don’t worsen the stability and precision of the former algorithm.展开更多
In this paper,we demonstrate that the double-shift QL algorithm for an irreducible anti-symmetric iridiagonal matrix with the shifts being two eigenvalues of the 2×2 matrix in the left upper corner of this matrix...In this paper,we demonstrate that the double-shift QL algorithm for an irreducible anti-symmetric iridiagonal matrix with the shifts being two eigenvalues of the 2×2 matrix in the left upper corner of this matrix is convergent and the convergence rale of Ms kind of algorithm is generally cubic.展开更多
QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O(n2) flops, to find all eigenval...QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O(n2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new.展开更多
文摘This paper establishes an improvement on the QL algorithm for a symmetric tridiagonal matrix T so that we can work out the eigenvalues of T faster. Meanwhile, the new algorithm don’t worsen the stability and precision of the former algorithm.
基金The author is supported by the State Major Key Project for Basic Researches of China the National Science Ponndation of China
文摘In this paper,we demonstrate that the double-shift QL algorithm for an irreducible anti-symmetric iridiagonal matrix with the shifts being two eigenvalues of the 2×2 matrix in the left upper corner of this matrix is convergent and the convergence rale of Ms kind of algorithm is generally cubic.
文摘QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O(n2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new.
文摘在大规模图结构数据中发现最稠密子图具有极其广泛的应用,如社区发现、垃圾邮件检测和论文引用关系抽取等。基于带标签的无向图,提出了查询标签集的概念,设计了一个可以快速发现最稠密子图的近似算法DSFLC(Densest Subgraph Finding based on Labelset Constraint):用户提交自定义的查询标签集,算法便可保证在用户可以接受的时间内返回满足查询标签集约束的最稠密子图。对于任何参数ε(ε>0),DSFLC算法只需扫描大规模数据集O(log1+εn)次,同时可保证算法的近似因子是2(1+ε)。对DSFLC算法进行分析后,发现该算法在预处理阶段易于并行化,因此选择Twitter Storm平台,并行化地实现了DSFLC算法。最后对从DBLP数据库中抽取的合作关系图进行测试,一方面研究Storm平台对算法的加速程度;另一方面分析挖掘出的子图的稠密度与参数ε之间的关系,最终验证了DSFLC算法的实用性和可扩展性。
