Zeros of polynomials: properties and applications

• Grant number: 12/08248-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2012
• End date: June 30, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Vanessa Avansini Botta Pirani
• Grantee: Evanize Rodrigues Castro
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

There are many areas of Mathematics where results concerning the behavior of zeros of polynomials are used to analyze certain problems. For example, in the study of the stability of numerical methods for solving differential equations, are important the results about the number of zeros that a polynomial has zeros on the unit circle. The control theory is another area where we can use results on the location of zeros of polynomials to analyze the stability of dynamical systems. So, the study of zeros of polynomials is a branch that has a wide range of applications and also many open problems, representing an inexhaustible source of research.(AU)