Robust Numerical Methods in Polynomial Algebra with Approximate Data

Northeastern Illinois University, Chicago IL

Investigators

Abstract

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.