Bernard J. Brommel Distinguished Research Professor of NEIU
Professor of Mathematics
NAClab 2019.8: Numerical Algebraic Computing Toolbox for Matlab
(updated on Aug. 31, 2019)
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
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.
MultRoot -- A Matlab
package for computing polynomial roots and
ACM Transaction on Mathematical Software, 30, pp 218-315, 2004 [Software Package]
A Newton's iteration quadratically converges to non-isolated solutions too, Preprint.
Main result: see the title.
On 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 applications. Part 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
Presentations (click the image to open the file, then keep clicking to see the animation)