期刊名称：International Journal of Computer Science Issues
印刷版ISSN：1694-0784
电子版ISSN：1694-0814
出版年度：2014
卷号：11
期号：1
出版社：IJCSI Press
摘要：In the paper we solve parametric linear systems of equations whose coefficients are , in the general case, nonlinear functions of interval parameters. Here solution means that we enclose the set of all solutions, the so-called parametric solution set, obtained when all parameters are allowed to vary within their intervals. This task appears in many scientific and engineering problems involving uncertainties. A C-XSC implementation of a parametric fixed-point iteration method for computing an outer enclosure for the solution set is proposed in this paper .This method requires to bound the range of a multivariate function over a given box and often delivers intervals which are too wide for practical applications. We computed tight enclosures of the parametric solution set by using a new generalized interval arithmetic which is an arithmetic for intervals (which are representing uncertainties). The most important property of this method is to reduce the effect of the dependency problem which is inherent in the computation with standard interval arithmetic. We used the new arithmetic to tightly bound the range of a multivariate nonlinear function over a box, a task to which many problems in mathematics and its applications can be reduced. We applied the new bounding technique to improve the efficiency of the solution for parametric systems. Numerical examples illustrating the applicability of the proposed method are solved, and compared with other methods.
