Computing with Composed Functions

本课题旨在利用组合函数的组合结构，开发有效求解由组合函数组成的方程组的理论、算法和软件。该项目将研究各种符号和数值运算的方法，如多元子结果、格罗布纳基、特征集和牛顿迭代，这些都是求解方程组的基础。在大多数中等到大规模的工程计算中，组合函数的出现是非常自然和频繁的。预计本研究结果将对科学和工业的系统解决产生广泛的影响。

This project aims to develop the theory, algorithms, and software for solving systems of equations made of composed functions efficiently, by utilizing their composition structure. The project will investigate methods for various symbolic and numeric operations such as multivariate subresultants, Groebner bases, characteristic sets, and Newton iterations that are fundamental to solving systems of equations. Composed functions arise very naturally and frequently in most moderate- to large-scale engineering computations. It is expected that the results of this research will have a broad impact on system solving in science and industry.