On Restarting the Arnoldi Method for Large Nonsymmetric Eigenvalue Problems

The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired. We analyze several approaches to restarting and show why Sorensen's implicit QR approach is generally far superior to the others. Ritz vectors are combined in precisely the right way for an effective new starting vector. Also, a new method for restarting Arnoldi is presented. It is mathematically equivalent to the Sorensen approach but has additional uses.

     

Diagnostics on LALR(k) conflicts based on a method for LR(k) Testing

A user of an LALR(k) parser generator system may have difficulties in understanding how a given LALR(k) conflict is generated. This is especially difficult if the conflict does not correspond to an LR(k) conflict.A practical method for giving informative diagnostics on LALR(k) conflicts is presented. The diagnostics distinguish between those LALR(k) conflicts that correspond to LR(k) conflicts and those that do not. As a side effect the user is thus informed whether or not his grammar is in fact LR(k) despite not being LALR(k).The method is based on an algorithm for testing LR(k)-ness using the LR(0) machine supplied with LALR(k) lookahead sets. This algorithm is presented and its correctness is proved.     

On the Randomized Error of Polynomial Methods for Eigenvector and Eigenvalue Estimates

In this paper we consider the problem of estimating the largest eigenvalue and the corresponding eigenvector of a symmetric matrix. In particular, we consider iterative methods, such as the power method and the Lanczos method. These methods need a starting vector which is usually chosen randomly. We analyze the behavior of these methods when the initial vector is chosen with uniform distribution over the unitn-dimensional sphere. We extend and generalize the results reported earlier. In particular, we give upper and lower bounds on the _pnorm of the randomized error, and we improve previously known bounds with a detailed analysis of the role of the multiplicity of the largest eigenvalue.     

非线性(k,n-k)共轭边值问题正解存在的特征值条件

该文在有关相应线性算子特征值的条件下,讨论非线性(k,n-k)共轭边值问题允许h(x)在x=0和x=1奇异．利用锥上的不动点指数理论获得了正解和多重正解的存在性．     

Geometric Estimates of the First Eigenvalue of (p,q)-elliptic Quasilinear System Under Integral Curvature Condition

Consider (M,g) as a complete, simply connected Riemannian manifold. The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of (p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold. In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.     

Differential quadrature method (DQM) and Boubaker Polynomials Expansion Scheme (BPES) for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems

The differential quadrature method (DQM) and the Boubaker Polynomials Expansion Scheme (BPES) are applied in order to compute the eigenvalues of some regular fourth-order Sturm-Liouville problems. Generally, these problems include fourth-order ordinary differential equations together with four boundary conditions which are specified at two boundary points. These problems concern mainly applied-physics models like the steady-state Euler-Bernoulli beam equation and mechanicals non-linear systems identification. The approach of directly substituting the boundary conditions into the discrete governing equations is used in order to implement these boundary conditions within DQM calculations. It is demonstrated through numerical examples that accurate results for the first kth eigenvalues of the problem, where k = 1, 2, 3, … , can be obtained by using minimally 2(k + 4) mesh points in the computational domain. The results of this work are then compared with some relevant studies.     

图的（k，d）-着色问题的一个近似算法

本文讨论了图的(k,d)-着色问题的算法,并给出了一个由四层神经元组成的神经网络算法.当一个图的循环色数已知时(不妨设为k/d),可以利用该算法成功地求出这个图的一个可行(k,d)-着色方案;当一个图的循环色数未知时,可以利用该算法求出这个图的循环色数的近似值.     

(1,k)-configuration facets for the generalized assignment problem

class of facet defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from (1,k)-configuration inequalities.Partial financial support under NSF grant #CCR-8812736.Partial financial support under NSF grant #DMS-8606188.     

关于S~(n p)(1)的紧致子流形的第一特征值(英文)

记H0 =maxx∈M｜H(x) ｜ ,其中H(x)为Sn p( 1 )的n维紧致子流形的平均曲率向量 .则其Lplace算子的第一特征值满足 :λ1≤n nH20 .     

关于f(k)f-a的零点之猜测

本文完全证明了[1]中的一个猜测，设f为超越整函数，k为非负整数，则f^(k)f仅可能有的Picard例外值是0，由此还得到整函数族的一个正规定则。     

A Generalization of a Two-Parameter Quantization for the Group GL 2(k)

We generalize a well-known two-parameter quantization for the group GL ₂(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL ₂(k).     

Upper (lower) bounds of the eigenvalues,spread and the open problems for the real symmetric interval matrices

This work is concerned with exploring the upper bounds and lower bounds of the eigenvalues of real symmetric matrices of order n whose entries are in a given interval. It gives the maximum and minimum of the eigenvalues and the upper bounds of spread of real symmetric interval matrices in all cases. It also gives the answers of the open problems for the maximum and minimum of the eigenvalues of real symmetric interval matrices. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐difference approximation for the u(k)‐derivative with O(hM−k+1) accuracy: An analytical expression

An approximation of function u(x) as a Taylor series expansion about a point x₀ at M points x_i, ～ i = 1,2,…,M is used where x_i are arbitrary‐spaced. This approximation is a linear system for the derivatives u^(k) with an arbitrary accuracy. An analytical expression for the inverse matrix A ^?1 where A = [A_ik] = (x_i ? x₀)^k is found. A finite‐difference approximation of derivatives u^(k) of a given function u(x) at point x₀ is derived in terms of the values u(x_i). © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Bounds on the maximum numbers of clear two-factor interactions for 2~((n1+n2)-(k1+k2)) fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolutionⅢorⅣunder the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods.     

A Minimal-Automaton-Based Algorithm for the Reliability of Con(d,k, n) Systems

A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's algorithm published in 1997, where . In this paper we use automata theory to reduce to . For d small or close to k, we have reduced from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is , where .     

P*(κ)阵线性互补问题一种新的宽邻域预估-校正内点算法

基于邻近度量函数的最小值,对P*(κ)阵线性互补问题提出了一种新的宽邻域预估-校正算法,在较一般的条件下,证明了算法的迭代复杂性为O(κ+1)23n log(x0ε)Ts0.算法既可视为Miao的P*(κ)阵线性互补问题Mizuno-Todd-Ye预估-校正内点算法的一种变形,也可以视为最近Zhao提出的线性规划基于邻近度量函数最小值的宽邻域内点算法的推广.     

Toughness condition for the existence of all fractional (a,b,k)-critical graphs

In this article, we obtain a sufficient condition related to toughness $\tau \left(G\right)$ for a graph to be all fractional $(a,b,k)$-critical. We prove that if $\tau \left(G\right)\ge \frac{(b^2?1)+ak}{a}$ for some nonnegative integers $a,b,k$, then $G$ is all fractional $(a,b,k)$-critical. Our result improves the known results in Liu and Zhang (2008) and Liu and Cai (2009).     

Optimized Dropping and Rolling (ODR) method for packing of poly-disperse spheres

Powder-based microstructures are traditionally modelled using densely packed spherical particles. In this letter, a new dropping and rolling packing algorithm is employed by means of analytical equations, to investigate the random packing of spherical particles. The three-dimensional randomly packed microstructures are quantified in terms of packing density and computational time.     

关于热方程U_t—c(x)(k(x)U_x)_x=0确定未知系数k(x)的一个反问题

本文讨论了热方程U_1—c(x)k(x)U_x)_x=0在区域x>0,t>0上确定未知系数k(x)的反问题,文中给出了局部解的存在,唯一性。