Interval Methods for Nonlinear Algebraic Systems--Techniquesand Software Based on Decomposition of Arithmetic Expressions and Preconditioning

因为，与其他方法相比，区间计算给出的结果具有数学上的确定性，即使在数据中存在不确定性、舍入误差和非线性的情况下，它们在科学、工程和运筹学中具有独特的潜在重要性。本项目的工作将通过以下方式促进这一潜力的实现。o将开发一个现代的、可移植的、标准化的基本函数库，与Fortran 90的运算符重载功能兼容，并与区间算术计算结合使用。为了更好地利用这种系统的结构，将实现一种解析代数方程非线性系统的技术，从而避免区间非线性系统解算器中的高估和低效。这些方法将应用于各种实际问题，包括鲁棒几何计算、机器人运动学、化学动力学平衡和化学炼油厂模型。

Since, in contrast to other methods, interval computations give results with mathematical certainty, even in the presence of uncertainty in the data, roundoff error, and nonlinearities, they are of unique potential importance throughout science, engineering, and operations research. The work in this project will advance realization of this potential in the following ways. o A modern, portable, standardized library of elementary functions will be developed, compatible with the operator overloading feature of Fortran 90, to be used in conjunction with interval arithmetic computations. o A parsing technique for nonlinear systems of algebraic equations will be implemented to better take advantage of the structure of such systems, and thus avoid much of the overestimation and resulting inefficiency in interval nonlinear system solvers. o The methods will be applied to various practical problems, including robust geometric computation, robot kinematics, chemical kinetics equilibrium, and chemical refinery models.