Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Finding roots of a particular multiplicity in high style

Speaker: **Yi Jin**, J. P. Morgan

Date: Thursday, March 9, 2006 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Many high order iterative root-finding algorithms such as Newton's method and Halley's method degrade to linear convergent algorithms when the root is of multiplicity greater than 1 (such a root is often called a multiple root). In this talk we show how to construct an algorithm of arbitrary integral order $m\geq 2$ for roots of a particular multiplicity gracefully, i.e., through an algebraic combinatorial approach.

(joint work with Bahman Kalantari)