Zeng

 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  9:00 - 11:00 am  (walk-in, no need for appointment)

                        
Links to current courses  [Math 165][Math 253]
 [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
 

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