论文标题
线性功能算术的开发及其在解决间隔分析问题上的应用
Development of linear functional arithmetic and its application to solving problems of interval analysis
论文作者
论文摘要
这项工作致力于构建新型的间隔 - 功能间隔。这些间隔建立在扩展从数字到函数的界限的想法上。功能间隔表明自己有望进一步研究和使用，因为与经典间隔相比，它们具有更丰富的代数特性。在工作中，线性功能算术是由一个变量构建的。将此算术应用于解决间隔分析的此类问题，因为在间隔上最小化功能并在间隔上找到函数的零。线性功能算术的数值实验的结果表明，使用新类型的间隔时，算法的收敛性高和更高的速度，尽管计算没有使用有关导数函数的信息。同样在工作中，根据几个变量的函数有理间隔的使用，修改了几个变量的最小化算法函数。结果，它得到了改进的算法加速，但只能达到一定数量的未知数。
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising for further study and use, since they have more rich algebraic properties compared to classical intervals lamy. In the work, linear functional arithmetic was constructed from one variable. This arithmetic was applied to solve such problems of interval analysis, as minimization of a function on an interval and finding zeros of a function on an interval. Results of numerical experiments for linear functional arithmetic showed a high order of convergence and a higher speed the growth of algorithms when using intervals of a new type, despite the fact that the calculations did not use information about derivative function. Also in the work, a modification of the minimization algorithms functions of several variables, based on the use of the function rational intervals of several variables. As a result, it was Improved speedup of algorithms, but only up to a certain number of unknowns.
