Robust Numerical Methods in Polynomial Algebra with Approximate Data

这个项目的目的是继续开发可靠、准确和有效的近似多项式代数的数值算法，以及扩展软件工具箱ApaTools的能力的实施。除了那些在以前NSF支持下开发的健壮算法/软件之外，PI还建议设计和实现三个基本代数问题的算法：多元多项式的近似不可约因式分解、多重数结构的识别和求解多项式系统的数值消元。这项研究将在计算机代数和数值分析的交叉点上进行，结果包括解决数学问题的算法和软件包。该项目的成果有望为机器人、分子构象、化学平衡、自动控制和其他数学分支(如代数几何)的应用领域提供关键工具。

This project aims at continuing development of reliable, accurate and efficient numerical algorithms for approximate polynomial algebra, along with implementations for expanding the capacity of a software toolbox ApaTools. In addition to those robust algorithms/software developed under previous NSF support, The PI proposes to design and implement algorithms for three fundamental algebraic problems: the approximate irreducible factorization of multivariate polynomials,identification of the multiplicity structure, and numerical elimination in solving polynomial systems. This research is to be carried out in the intersection of computer algebra and numerical analysis with an outcome consists of algorithms and software packages for solving mathematical problems. The results of this project are expected to supply critical tools for application areas such as robotics, molecular conformation, chemical equilibrium, automatic control, and other branches of mathematics such as algebraic geometry.