Zhonggang Zeng  
Bernard J. Brommel Distinguished Research Professor of NEIU
Professor of Mathematics

Office: 218D,
 Science Building,    Phone: (773)442-5763     email: zzeng at neiu dot edu

Office hours:  Monday & Wednesday  10:00-12:00, 2:30-3:30  (walk-in, no need for appointment)

Links to current courses  [Math 253][Math 304]
 [Math 340]

NewNAClab 2019.8:  Numerical Algebraic Computing Toolbox for Matlab 
                                    (updated on Aug. 31, 2019)

Research projects:
supported in part by National Science Foundation under Grant DMS-1620337 
(Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s)
and do not necessarily reflect the views of the National Science Foundation

Software release  ApaTools a software toolbox for approximate polynomial algebra in Maple 

Selected publications:

Computing multiple roots of inexact polynomials,  Mathematics of Computation, 74(2005),  pp 869 - 903
                This work won the Distinguished Paper Award
at ACM ISSAC '03 Conference
            Main result:  Multiple roots can be computed accurately from perturbed polynomials in numerical computation.
          The citation:
             citation                 award       

Algorithm 835: MultRoot -- A Matlab package for computing polynomial roots and multiplicities, 
ACM Transaction on Mathematical Software, 30, pp 218-315, 2004    [Software Package]

NewA Newton's iteration quadratically converges to non-isolated solutions too,  Preprint.
Main result:  see the title.

NewOn the sensitivity of singular and ill-conditioned linear systems,  SIAM J. Matrix Anal. Appl., 40(2019) pp. 918-942
Main result:  Singular linear systems are not necessarily ill-conditioned.

The numerical factorization of polynomials   J. of Foundation of Computational Mathematics
Main result:  Numerical polynomial factorization is a well-posed problem that can be accurately computed.

 Sensitivity and computation of a defective eigenvalue     [Resources / Matlab codes]  SIAM  J. Matrix Anal. Appl.
                              Main result:  A defective eigenvalue can be regularized as a well-posed problem that is accurately solvable.

Multiple zeros of nonlinear systems   Mathematics of Computation,  
Regularization and matrix computation in numerical polynomial algebra  
A rank-revealing method with updating, downdating and applicationsPart I  &  Part II
SIAM Journal on Matrix Analysis and Applications
The approximate GCD of inexact polynomials   Part I  Part II 
A numerical elimination method for polynomial computations  Theoretical Computer Science
The closedness subspace method for computing the multiplicity structure of a polynomial system


Other publications

Presentations (click the image to open the file, then keep clicking to see the animation)

       The Tale of Polynomials     Removing Ill-posedness    Approximate GCD