摘要:

In the paper, a characterization of simple period doubling points of a discrete dynamical systemxk:+l=f(xk, λ)f:ℝn× ℝ → ℝnby a set of singularity and nondegeneracy conditions is given. These conditions reduce to those given in the book of Gucken-heimer/Holmes [83] for the scalar casen= 1. Based on this characterization, a minimally extended systemG(x, λ) = 0 for defining period doubling points is proposed.Itconsists of the fixed point equationf(x, λ)−x= 0 and a certain singularity conditiong(x, λ) = 0g: ℝn× ℝ → ℝnMoreover, an analogously constructed minimally extended system for pitchfork bifurcation points is given, and the relation between pitchfork bifurcation and period doubling points is discussed. The minimally extended system is used for computing period doubling points by Newton-type methods. The solution of the linear systems required in Newton's method is realized by a block elimination technique similar to that introduced by PÖNisch/Schwetlick [81]. The performance of the algorithm is demonstrated on hand of a periodically excited Duffing oscillator where the Feigenbaum sequence of period doubling points is computed up to period 32

ISSN:1055-6788    

DOI:10.1080/10556789708805663

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

A nonmonotone strategy for solving nonlinear systems of equations is introduced. The idea consists of combining efficient local methods with an algorithm that reduces monotonically the squared norm of the system in a proper way. The local methods used are Newton's method and two quasi-Newton algorithms. Global iterations are based on recently introduced box-constrained minimization algorithms. Numerical experiments are presented

ISSN:1055-6788    

DOI:10.1080/10556789708805664

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Reverse automatic differentiation provides a very low bound on the operations count for calculating a gradient of a scalar function inndimensions but suffers from a high storage requirement. In this paper we will show that both can often be greatly reduced. This will be illustrated using the inverse diffusion problem. This problem involves the solution of partial differential equations using finite elements, the solution of many sets of linear equations by Choleski decomposition, which together lead to the solution of a nonlinear least squares optimisation problem by conjugate gradients. The approach described here has enabled the gradient of this problem to be obtained at a small fraction of the operation count of the function evaluation and reduced the store required to evaluate the gradient to the same order as that required to evaluate the function. Similar results are given for the directional second derivative

ISSN:1055-6788    

DOI:10.1080/10556789708805665

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper we consider an inverse minimum spanning tree problem in which we wish to change the original weights of the edges in a graph as little as possible so that a given spanning tree of the graph can become the minimum spanning tree. An algorithm is proposed which can solve the problem in polynomial time. The algorithm is a combinatorial method that uses the minimum covering problem as its main subproblem. An example is included to illustrate the method

ISSN:1055-6788    

DOI:10.1080/10556789708805666

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789708805662

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor