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This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalentconstrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In this article, we investigate some theoretical and computational issues of the geometric buildup algorithm proposed by Sit, Wu and Yuan (Bull. Math. Biol. 71:1914-1933, ) for the solution of the distance geometry problem with sparse and inexact distances. This algorithm repeatedly uses a least-squares approximation to determine the position of an undetermined atom, using the distances from this atom to a set of previously determined ones. The least-squares approximation, obtained from the singular value decomposition of a distance-induced matrix, can find the best possible position for the atom, even if the distances have small errors, as they usually do in practice, and therefore make the geometric buildup algorithm more stable than its previous versions that relied on linear system solvers. We estimate its numerical errors and prove some of its key mathematical properties. We also present some numerical results with varying some of the parameters in the algorithm and show how they may be used to improve its performance and computational accuracy. [ABSTRACT FROM AUTHOR]

This article gives a trajectory-following method for the steady state of chemical reaction rate equations. In order to avoid wasting unnecessary computing time during the steady-state phase and get roughly accurate solutions during the transient-state phase, this method is realized via adopting the semi-implicit Euler formula as the stepping direction and adaptively adjusting the time-step size by an analogous trust-region technique. Under some standard assumptions, its global convergence analysis and local superlinear convergence analysis are also given. Finally, some numerical experiments of this method, in comparison with the traditional optimization methods and ordinary differential equation methods, are reported. The numerical results show that this trajectory-following method is a promising solution for this class of problems. [ABSTRACT FROM AUTHOR]

A new 3D fingerprinting positioning scheme based on cellular networks is proposed by using implicit information of the location around geographic environments. Compared with original fingerprint positioning scheme, singular measurement is processed at the beginning of the proposed scheme. The main improvement of our proposed scheme is to employ cell matching degree and choose the best reasonable fingerprint according to the correlation of its surrounding points. Additionally, in order to improve searching efficiency, a new searching window is introduced. Finally, compared with the maximum likelihood method and the weighted K nearest neighbors method, the promising numerical results are also presented. [ABSTRACT FROM AUTHOR]