POWRE: Studies of Zeros of Polynomials and Systems of Analytic Maps

Suny College At Old Westbury, Old Westbury NY

Investigators

Abstract

The PI will work on solving polynomials and systems of polynomials. Polynomial equations and systems are used in many areas of scientific computing and engineering: mechanism theory, robotics, chemistry. The development of efficient and reliable algorithms for solving these problems are important particularly for systems with a large number of variables. The goal of this project is to extend the path lifting method which is well understood in the case of a single variable equation, to a system of polynomials. She will begin with a special case of a map from a Riemann surface. For the more general case, she will work jointly, with teams at Toulouse and at Stony Brook and communicate with S. Smale, F. Cucker(Hong Kong) and M. Shub (NY). This plan includes implementing this algorithm, large scale experiments involving various types of Newton method and choices of initial points. We will gather numerical evidence in terms of complexity and in terms of stability with respect to finite precision computations. POWRE will supports her visit to City University of Hong Kong, IBM Watson Center, and Toulouse to collaborate (and consult) with experts in the field. Under POWRE, PI will mentor 3 undergraduate students including two minority students at SUNY at Old Westbury to develop their academic interests towards graduate studies in mathematics. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).