摘要:

In one approach to automatic differentiation, the range of a function is generalized from a single real value to an aggregate representing the values of the function and one or more derivatives. The operations and functions of elementary analysis are extended to these aggregates so as to preserve the validity of the derivatives. In this paper we develop a recursive approach to defining the necessary operations in the context of functions of several variables. Formally, the definitions are essentially the same as those needed in the single variable case. The resulting system provides automatic propagation of values of all partial derivatives up to a prespecified order for a function of several variables

ISSN:1055-6788    

DOI:10.1080/10556789508805632

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

The numerical problem of estimating unknown parameters in systems of ordinary differential equations from complete or incomplete data is treated. A new numerical method for the optimization part, based on the Gauss-Newton method with a trust region approach to subspace minimization for the weighted nonlinear least squares problem, is presented. The method is implemented in the framework of a toolbox (called diffpar) in Matlab and several test problems from applications, giving non-stiff and stiffODE-systems, are treated

ISSN:1055-6788    

DOI:10.1080/10556789508805633

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

All the new interior-point algorithms for linear programming (LP) assume that the rows of the constraint matrix are linearly independent. The assumption is necessary, because the algorithms solve a certain linear system which does not have a unique solution in the case of dependent rows. In this paper we study a pivoting based approach for finding all the linearly dependent rows. Moreover encouraging computational results are reported

ISSN:1055-6788    

DOI:10.1080/10556789508805634

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this paper, a criterion of feasibility and existence of the optimal solution is suggested as the basis for a unified general approach to the solution of eight classes of the integer programming problems with inaccurate data arising from the study of actual problems with a dynamic nature of the described processes, an uncertainty of the available information, etc. A method is also described which can be applied to the solution of twelve classes of the above problems under a certain assumption. The obtained results can be used for solving practical problems, for example, decision making, integer programming, as they enable to reduce such problems to simpler models. These results may prove to be useful for theoretical analysis of the mentioned problems, for example, when studying the stability of the integer programming problems solution

ISSN:1055-6788    

DOI:10.1080/10556789508805635

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789508805631

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor