Adaptive selection of parameters for precise computation of matrix exponential based on padé approximation

讨论了基于Pad\'{e}逼近的矩阵指数精细积分方法中加权系数N 和展开项数q的自适应选择问题. 参数(N,q)的选择直接影响到矩阵指数计算的精度和效 率. 采用矩阵函数逼近理论，研究了参数N和q的增加对精度的影响程度，据此，提出了 参数(N,q)优化组合的递推自适应选择方法. 该方法可以根据矩阵本身的性态选择合适的参 数(N,q),而参数选择的计算量与矩阵指数的计算量相比几乎可以忽略，这对于增强矩阵指 数精细积分方法的适应性和提高计算效率是很有益处的. 算例验证了该方法的正确性和有效性.     

An Affine Scaling Interior Trust Region Method via Optimal Path for Solving Monotone Variational Inequality Problem with Linear Constraints

Based on a differentiable merit function proposed by Taji et al. in ＂Math. Prog. Stud., 58, 1993, 369-383＂, the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.     

Finite-size scaling corrections for the eight-vertex model

Finite-size scaling corrections are calculated analytically for two of the maximal eigenvalues of the transfer matrix in the isotropic eight-vertex model. The valuec=1 for the conformal anomaly of the Virasoro algebra is confirmed.     

On the metric properties of the Feigenbaum attractor

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.     

AN ASYMPTOTICAL O((k + 1)n~3L) AFFINE SCALING ALGORITHM FOR THE P_*(k)-MATRIX LINEAR COMPLEMENTRITY PROBLEM

1. IlltroductionAn LCP is normally for finding vectors x, s E Wu such that:where q E aam and M E Rrsxn. An LCP is called monotonic if M is positive semi-definite. Inthis paperg M is assumed to be a P*(K)--matrir[6][9] i.e. for a K 2 0, M satisfies:for any u E ac. Obviouslys positive semi-definite matrix is a p*(0)-matrix. It wajs proved in[10] that M is a P*(K)--matrix if f M is a sufficient[1].Based on Dikin's approach, Monteiro and Adler proposed in [81 an affine scaling algorith…     

Scaling spectra and return times of dynamical systems

The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by the close return times of the dynamical system described. Thus, an intimate connection exists between the shape of the singularity curve and a small but interesting set of dynamical properties.     

Superlinearly convergent affine scaling interior trust-region method for linear constrained LC<Superscript>1</Superscript> minimization

We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.     

Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang （KPZ）, Sun-Guo-Grant （SGG）, and Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.     

Kq, Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility ξ(T) agree with the scaling relations of experimental data.